On 30 June 1972 Pablo Picasso created his last self-portrait. He had depicted himself many times before, but never like this. His face looked like a skull with stubble. Its colour was greenish-grey. The mouth was a straight slit. Only the lines under his eyes proved his features were flesh and not raw bone, which seems to protrude from his head at the left of the picture, where it is set against red fire, blood, or a setting sun.

From his youthful self-portraits to his bare-chested appearance, at the age of 75, in Henri-Georges Clouzot’s 1956 film The Mystery of Picasso, the artist, so fit and long-lived, enjoyed showing off his muscular body. But in his last images of himself, the shoulders that were still so powerful when he displayed them in Clouzot’s adoring film had shrunk to the dried flatness of a mummy. This was his 91st year. Picasso looked at himself without illusions, underlining the true state of things with heavy black lines.

When friends came to visit he would show them the self-portrait of 30 June. It had pride of place on an easel apart from his routine clutter. He wanted to know how others saw it.

Picasso habitually studied his own works in this meditative way: his studio, and all his homes, were filled with his own artworks, going right back to juvenilia from his teenage years in Spain. He kept a bank vault in Paris, filled with paintings, prints, sculptures, and even poetry. But his self-portrait as a death’s head was something else; he kept goading friends to interpret it, insisting they gaze with him into its big terrifying eyes. This picture of a death foreseen was, for Picasso, “a mirror”, his friend and biographer John Richardson told me.

Less than a year after making it, he died, at home in Mougins in the south of France, on 8 April 1973. He was buried at the foot of Mont Sainte-Victoire in Provence, in a striking final homage to Cézanne – whose hesitant, searching paintings of this mountain did so much to inspire Picasso’s cubist revolution in the early years of the 20th century.

He was survived by his second wife, Jacqueline, as well as his “legitimate” son by his first marriage, Paulo, and Paulo’s three children, Pablito, Marina and Bernard. Then there was his former lover Marie-Thérèse Walter and their daughter Maya. And Françoise Gilot, the author of Life with Picasso, a merciless picture of an ageing artist lording it over his much younger lover, rich with embarrassing details of his habits and opinions – such as his insistence that one cannot be a real woman without becoming a mother. After failing to prevent its publication in 1964, Picasso tried to cut their children, Paloma and Claude, out of his life.

He also left 1,876 paintings, 1,335 sculptures, 7,089 standalone drawings, 18,000 prints, 2,880 ceramic pieces and 149 notebooks of drawings. It was the greatest collection of Picasso’s art in either private or public hands.

After his death, the vast personal collection that was discovered in his various studios and homes befuddled even his closest friends and most intimate students. No one had known the scale and substance of this private dimension to Picasso’s genius. It was not just the stupefying quantity of works he kept, but how and why he kept them, which had no equivalent in art.

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The collection that Picasso left behind came to about 70,000 items. But it took nearly a decade to sort out his legacy. First, the rights of his children and grandchildren had to be established – hardly a simple matter. Picasso loved fatherhood, as his portraits of his children demonstrate, but he performed its duties inconsistently. As the diverse and fragmented Picasso family tried to settle the estate, they suffered a series of misfortunes that still offer the darkest possible material to those who see the painter of Guernica as a misogynist who ruined the lives of his wives, mistresses, children and even grandchildren. His grandson Pablito died from drinking bleach a few days after being refused admittance to Picasso’s funeral by his second wife, Jacqueline, who kept out everyone but herself and his eldest son. Pablito’s father Paulo died in 1975, after a life wrecked by alcohol. Marie-Thérèse Walter, the lover whose opulent body is the theme of some of his wildest art, hanged herself in 1977. Nearly a decade later, in 1986, Jacqueline herself committed suicide.

Even in his lifetime, Picasso saw his private life become unpleasantly public. It is sometimes implied his lovers were passive victims of his demanding, even childish character but more than one of them got her own back in print. Fernande Olivier, the lover of Picasso’s youthful days in Montmartre, was first to publish in 1930. Gilot caused even more of a sensation with her revelations. In 2001, Marina Picasso, Paulo’s daughter, published a book accusing her grandfather of damaging her childhood, first by crushing her father’s character, and then by refusing adequate financial help to a family he knew to be struggling.

Out of the infernal soap opera of the Picasso family in the 1970s, Claude Picasso, the painter’s only surviving son, emerged as the leader of the family and took a highly influential role in shaping Picasso’s artistic legacy.

In 1979, the Picasso family made a huge donation of Picasso’s Picassos to the French state in lieu of inheritance tax. Crucially, public curators were given first choice of the inheritance – they could pick the very best of Picasso’s personal collection to represent his entire career. After touring the world to universal acclaim, this mesmerising addition to the French patrimoine national was given a permanent home in the Hôtel Salé, a fine classical 17th-century building in one of the best-preserved parts of pre-modern Paris. The Picasso Museum opened in 1985, with a collection of 5,000 works by Picasso and an archive of some 200,000 items.

Pablo Picasso’s only surviving son, Claude. Photograph: Sebastien Bozon/AFP

Picasso did not merely inscribe his paintings and drawings with the year they were made; many of them were dated to the month and the day. The works he kept for himself tended to have a still greater documentary significance: they were often his first efforts in a new style, gutsy experiments with some new idea. He did not only keep truckloads of his own work, he carefully oversaw its documentation. As early as 1932, when he still had four decades of creativity ahead, Picasso worked closely with the Greek critic Christian Zervos on the first volume of what was to become a 33-volume catalogue raisonné of his output and a model of this type of reference book. He also kept a vast private archive.

Every Picasso researcher relies on the Picasso Museum. “It’s such an astounding collection,” the eminent art historian TJ Clark told me, “and all the time it provokes questions. Why did he hang on to these pictures in particular?” John Richardson called it “the greatest collection of Picassos in the world”.

This is, in effect, a museum curated by Picasso himself. He originally chose everything in it – including his personal collection of works by such artists as Degas, Cézanne and Henri Rousseau – and it contains, like a magical cabinet, the ceaseless energy of his life and art. But in the past few years, the institution created to preserve and display Picasso’s unrivalled collection of his own work has also been engulfed by crisis and scandal – touched by the tumult of yet another impassioned battle over the ownership of the great artist’s legacy. It has been closed since 2009, with work on a renovation running years overdue amid recriminations and allegations of mismanagement. In May of this year, another delay was announced, and the museum’s president, Anne Baldassari, was sacked by the French government. It is finally due to reopen on 25 October, amid a frankly surreal atmosphere of accusation and dissent.

The turmoil at the museum comes at a suggestive and perilous moment for Picasso’s wider legacy. Is the most revolutionary and exciting artist of the 20th century still a living force in the 21st? Crowds still pack travelling exhibitions of his work, which continues to command astronomical prices at auction. But while the playful spirit of his contemporary, Marcel Duchamp – who began his career in a particularly dim corner of Picasso’s giant shadow – still inspires and shapes artistic creation, it is far harder to discern Picasso’s direct influence among today’s most celebrated contemporary artists. Do we still feel Picasso as a kick in the stomach, a shattering visionary, or has he slipped away from us into the safeness of history – to become an Old Master, deeply revered but as far away from the present as two of his own heroes, Velázquez and Poussin, are generally held to be?

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In 1992, seven years after the museum opened, Anne Baldassari came to work in its archives. The 37-year old doctor of arts and social sciences had previously been at the National Museum of Modern Art in the Pompidou Centre, just a few streets away from the well-preserved streets of the Marais quarter where the Musée Picasso can be found. She is, she told me, “a crazy researcher”, and in the Picasso Museum’s unrivalled, intimate collection of documents she soon made spectacular discoveries. For instance, among Picasso’s hoards of news clippings and notes she found that he was a serious photographer.

“I discovered his negative plates,” she recalled. “It’s very interesting especially about cubism: experiments in double exposure that he did in 1909.” In other words, the cubist revolution with its breaking up of the traditional picture into a hint of a bottle or a glimpse of a musical note amid labyrinths of painterly dapples and swerving angles may be connected to his interest in photographic effects. Baldassari’s research on Picasso’s camera culminated in an acclaimed exhibition in 1997, which permanently made photography part of the way his art is seen.

Even more dramatically, she found a series of postcards in the museum archive that date from 1906 and carry photographs of African women by François-Edmond Fortier. 1906 is a year before Picasso painted Les Demoiselles d’Avignon, his scything pink and blue vision of jagged-limbed glaring prostitutes, two or perhaps three of whom wear what appear to be African masks. Do the “primitive” poses of Picasso’s wild women mirror Fortier’s photographs? Are these pictures the surprisingly simple – and colonial – source of the 20th century’s first great artistic earthquake?

The striking research Baldassari produced made her one of the world’s leading authorities on Picasso. Her services as a curator were widely sought after, her reputation truly international. “She loves her Picasso,” the art critic and broadcaster Waldemar Januszczak, who has followed her career with admiration, told me. In 2002, she was one of the organisers of Matisse Picasso, a blockbuster staged jointly by Tate Modern, New York’s Museum of Modern Art, the Pompidou and the Picasso Museum, which is widely regarded as one of the all-time great exhibitions of modern art.

Anne Baldassari at the Picasso Museum in Paris Photograph: Felix Clay

Baldassari’s appointment as director of the Picasso Museum in 2005 was the logical next step. She had already raised its status as a museum – with her there, its exhibitions were seen as essential. Baldassari continued to curate important Picasso shows in and beyond the museum, including the immense Picasso and the Masters at the Grand Palais in 2009. Yet by this time her ambitious curatorial approach was attracting criticism as well as praise. The respected art critic Richard Dorment called Picasso and the Masters “a complete and utter failure, an expensive turkey, the art world’s answer to Heaven’s Gate”. He was not the only one to find it an overblown sprawl that failed to do justice to either Picasso or the masters.

Baldassari was starting to attract personal criticism as well. Museums had trouble borrowing art, and scholars found it hard to research in the archives. “Anne Baldassari was a total menace,” John Richardson said. “She was loathed by Picasso scholars. She was no help whatsoever – she was a positive hindrance. You couldn’t see things in the library. Suddenly they weren’t available.” She would not loan works to other museums and “if she did loan things she came with them, which wasn’t much fun.”

Richardson even questions the quality of Baldassari’s own research. He thinks her use of French colonial postcards to “explain” Les Demoiselles d’Avignon is nonsense, and has confused a generation of students. He claims there is solid evidence in the Picasso Museum itself that Picasso owned these photographs only from 1911, several years after he painted Les Demoiselles d’Avignon.

Tales of Baldassari’s imperiousness circulate widely in the art world. One person told me that she once kept the director of a Russian museum, who had flown to Paris to discuss a loan of some works, waiting outside her office for a day before letting it be known she was too busy to meet. Another source claimed that a group of leading museum directors discussed writing a joint letter to the French culture ministry complaining about the leadership of the Picasso Museum. Whatever the truth of such rumours, they reveal that as Baldassari’s prominence and power increased, so did her enemies.

She did, however, have one very powerful friend.

“All the little anecdotes of when I was a child are bullshit essentially,” Claude Picasso told me, as we sat in bright September sunlight outside a neighbourhood restaurant in Paris – dismissing the notion that there was anything to be gleaned about Picasso, or his work, from the memories of his children. They must certainly be complex memories. In one of the sweetest paintings in the museum, done in 1954, when he was about seven, Claude is drawing while his sister Paloma plays close by. Picasso painted several similarly endearing images of his youngest children. But when their mother, Françoise Gilot, left him, called him a “historical monument”, and portrayed him in her book as a vain old fool, he punished the children in response.

Anne Baldassari was a total menace. She was loathed by Picasso scholars. She was no help whatsoever John Richardson

For all that, Claude Picasso not only inherited his share of the Picasso fortune, but took the leading role in the management of Picasso’s artistic estate. “Claude plays a very important part,” as Baldassari told me. Like her, he has sometimes been a controversial guardian of the Picasso legacy. When he licensed the name Picasso to Citroën for the new Picasso car in 1998, the legendary photographer Henri Cartier-Bresson wrote to Claude and accused him of having betrayed the legacy of a great artist who was also a member of the Communist party. “It was a private letter,” Cartier-Bresson told me at the time. “I sent it to Claude and I never got an answer.” The car turned out to be a great success, and the Picasso Administration, which Claude founded in 1995, has been highly effective at monetising the inheritance: no artist’s work costs more to reproduce in books or the media.

Meeting Claude Picasso produces a shock of recognition: he is such an exact physical replica of his father that sitting beside him is like meeting the spectre of old Pablo. He shares those fiery eyes, that Mediterranean skin, the wise simian face and unimposing stature. Our meeting had not been planned, but it was not a coincidence: Anne Baldassari had brought him along to lunch, in a dramatic display of her support from the leader of the Picasso clan.

In fact, more than one person I spoke to said that Claude Picasso’s friendship – so strikingly paraded before me – was the only thing that protected her as she made one enemy after another. Insiders don’t want to criticise him out loud because he is so influential in the loftiest Picasso circles. “Claude Picasso was the only person who stood up for her,” one person said. “Nobody else felt that way. Why does Claude back this woman who has done all these terrible things?”

But in 2010, Baldassari was promoted to become the Picasso Museum’s president – a position in French national museums whose power is unrivalled in comparable institutions in Britain or the United States. Answerable only to the French state, museum presidents do not have to negotiate with boards of trustees; some even have inner councils called cabinets. They rule their museums exactly as their title implies. By this time, however, Baldassari had taken a decision that would leave the museum, and her, in very deep trouble.

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When the Picasso Museum closed for renovation in 2009, Baldassari’s plan was to vastly enlarge the display space inside the 17th-century Hôtel Salé, which had originally been converted into a museum in the 1980s and always had a pleasantly stuffed, intimate feeling to it. She raised funds for the transformation by staging Picasso shows abroad – but a two-year project turned into a three-year one, then four years, then five.

Even though her supporters point to the €31m she raised through loan exhibits for the rebuilding, by this year, costs had risen to €52m. But the money was the least of the troubles. The museum announced a series of opening dates, with one after another postponed. It came to be regarded as a national embarrassment that one of France’s best-loved museums remained closed – and Baldassari began to bear most of the blame. By 2013, criticism of her management was no longer an art-world secret.

Early this year Vincent Noce, the art critic of the French paper Libération, published a leaked internal report that had severely criticised Baldassari. “She was interfering in everything, even in fields she knows nothing of,” Noce said. The report, he told me when we met in Paris, “said she had a real psychological problem”.

As the conflict inside the Picasso Museum started to spill into the media, the French state took an acute interest in its problems. Aurélie Filippetti, France’s minister for culture and communications, appointed a consultancy to investigate the situation; they reported that Baldassari refused to change her management style. “There was a social emergency” inside the museum, Filippetti told me. “She had very bad relations with other museums.”

Finally, on 11 May, Noce revealed in a second Libération scoop that more than half of the museum’s 40 staff members had signed an email demanding Baldassari’s dismissal, accusing her of “authoritarianism, partiality and managerial methods which have led the Picasso Museum into an impasse”. The gossip traded by Baldassari’s critics had become world news. “The mental and physical health of dozens of officials,” the staff letter continued, “and the world reputation of a museum which is already seriously isolated, cannot continue to be under threat in order to keep one sole person in office, which is now unjustified.”

Two days later, Filippetti summoned Baldassari to her office. “It was not a pleasure to have to ask her to resign,” Filippetti told me. “She’s a good curator but she was not a good president. Many people had quit and were not able to work with her any more. The person in charge of the building workers had quit. She had pushed two second-in-commands to quit. Nobody was able to work with her on the building. The museum could not open with her as president. That became clear at the beginning of the year.”

It seemed to Filippetti that as things stood the museum would never reopen. “In May there were wires everywhere,” Noce said. “No computers, no furniture, no safety system, no climate control. The entrance to the paintings was blocked by cables.” It had already taken far longer than anyone expected. “She was not good at managing people,” Filippetti concluded. “The Picasso Museum was not working.”

Filippetti offered Baldassari a lesser role, working strictly as a curator, so that she could stay on and organise the opening show – an idea, I was told, that had been endorsed by Laurent Le Bon, who was chosen to replace Baldassari as president. He told me he had “fought” for her to take on a curatorial role.

When she refused the offer – reportedly in a less than restrained manner – she was sacked the same day.

By the time I sat down to lunch with Anne Baldassari and Claude Picasso in September, the story had entered yet another phase. For one thing, Filippetti was no longer culture minister: she had been sacked by François Hollande at the end of the summer, as he tried to take his deeply unpopular administration in a more austere direction. Meanwhile, Baldassari had just spent her morning doing what she loves – curating Picasso at the Picasso Museum.

Baldassari agreed, after months of mutual antagonism and even a claim – never legally tested – that she had a right of authorship in the opening hang, to come and work on installing the new show. She’d just arranged the first room when we met. “I am happy, I can have lunch,” she said.

A slight woman who lives up to the image of a French intellectual, Baldassari turned out to be anything but a dry curatorial bureaucrat. Nor was she recognisable as an art-world monster – a species I have often encountered, the sort who shout at underlings to impress journalists in their company. As we discussed the epic and exciting task of redisplaying the museum’s collection, her intimate knowledge of the work was clearly infused with feeling.

“The collection is particularly strong in the surrealist period,” she said. This was a strange and provocative phase of Picasso’s career, when he was making works so violent or erotic – and often both – that he could not sell them. These profoundly personal works, tumultuous in their savage iconography of love and hate, stayed with him, and ended up in the Picasso Museum. They include his 1925 painting The Kiss, in which a couple appear to be eating one another as their bodies merge in carnivorous union, and the 1929 Nude in a Red Armchair, depicting a monstrous figure who screams at the sky baring stumps of teeth.

Picasso’s surrealist years, which can only be fully understood at the Picasso Museum, go to the heart of what still makes him shocking and scintillating. Many of the works in the museum date from between 1924 – when Picasso’s friend André Breton published his Surrealist Manifesto – and the end of the second world war, years in which he also played with found objects in a way that has inspired artists from Robert Rauschenberg to Damien Hirst.

Picasso’s 1942 Bull’s Head on display in the Picasso Museum. Photograph: Felix Clay

His 1942 sculpture Bull’s Head, a treasure of the Picasso Museum, was assembled in the misery of wartime Paris from a bicycle seat and a pair of handlebars – bits of rubbish that he turned into a mythic head, as much minotaur as bull. It is as if the painted ice age bulls in Lascaux cave, discovered in the Dordogne in 1940, put their magical charge into these relics of an old bicycle. Claude recalled Picasso laughing about it: “My father always thought it would be funny to take this thing and throw it back into the garbage pile, and see if anyone would make a bicycle out of it.”

Picasso’s trash bull is one of a succession of daring objects he made in his surrealist years that survive – despite their fragility and apparent ephemerality – in the museum. There are guitars made from scraps of cloth and newspaper in 1926. There is a 1930 tableau called Composition with Glove from which a grey three-dimensional hand spookily emerges. But what most arrests the viewer of his surrealist art is its lascivious, diabolical eroticism.

“Picasso said, ‘All my art is erotic’,” Baldassari noted. “You can find it anywhere.” Sex pulses through works in the museum collection, from his 1901 sketch Couple Entwined to his 1969 painting Woman with a Pillow, but Picasso’s sexual imperative is at its most overwhelming in his art of the 1920s and 30s. Fleshy bathers and barbaric nudes dominate the art of this era along with the minotaur, his self-image as an uncontrollable beast. In Picasso’s 1931 painting Figures on the Seashore, two bodies made of points and curves embrace in enigmatic ecstasy. For Picasso, Baldassari insisted, eroticism was “le sel de la vie, the salt of life. This is a way for him to have a discussion with us. We know about sex, we are sexual creatures, so it’s a common language.”

To discuss Picasso’s art with Anne Baldassari is inspiring; in her presence, it is almost difficult to believe that a person who knows this collection as if it were a part of herself could have been to blame for throwing it into crisis.

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Picasso’s art lives in the Hôtel Salé, but the artist himself lived for two decades in the attic of a grand house on Rue des Grands Augustins, near the Pont Neuf, at the heart of Left Bank Paris – in an apartment found for him by his lover Dora Maar in 1937. The first thing he painted here was a mural-scale masterpiece for the Spanish Pavilion at the Paris International Exhibition. The town of Gernika in northern Spain, the ancient capital of the Basques, had been bombed by the Luftwaffe on behalf of General Franco’s authoritarian revolt against the democratic Spanish Republic. It was here, in this old French house, that Picasso painted Guernica.

Looking up through a closed gate at the dilapidated windows of Picasso’s attic, it is strange to think that in this quiet corner of the city he created the most powerful political artwork of modern times. Picasso took all the imagery spewing from his unconscious in those surrealist years - the bulls, gored horses, broken bodies and screaming women - and turned his private phantoms into public symbols of suffering. Picasso’s savage side let him delve into the most primitive of feelings and images to create a work of universal anguish. He once berated the psychoanalyst Jacques Lacan for reducing the tragic human condition to mere sickness. Picasso believed in tragedy and could inflict it – as with the tears he provoked in Dora Maar, not least when he reduced her and Marie-Thérèse Walter to wrestling over him in front of the unfinished Guernica, helped him paint the heartbreaking faces of his Weeping Women. With Guernica, he gave the modern world its greatest work of tragic art.

The Picasso Museum in the Marais quarter of Paris. Photograph: Felix Clay

He would live and work here right through the second world war. In 1944 when Paris was liberated, it was here that American GIs and international reporters came to see for themselves the legend who had refused to let the Nazis scare him to America or prevent him working - the most harrowing work in the Picasso Museum is the terrifying 1943 bronze Death’s Head, which intuits the facts of the Holocaust as brutally as any work of art can do.

Yet even amid these years of drama and anguish, the loft embodied a comic thought, for this very building was the setting for a fictional story about art and madness that fascinated him. “On a cold December morning in the year 1612”, begins Balzac’s novella The Unknown Masterpiece, “a young man whose clothes looked threadbare was walking back and forth in front of a house in the Rue des Grands Augustins.” The young man is the future titan of art Nicolas Poussin, and inside he meets a master he wishes to learn from. But they are both mocked by an elderly painter who despises everyone else’s efforts, because he is painting the ultimate work of art: a nude so consummate it exceeds every other painting in history. It is his life’s work. But when they finally see it, the other artists find that his obsessive efforts have led to mad chaos. The painting is an indecipherable network of daubs and scrawls.

Picasso illustrated The Unknown Masterpiece in 1927, and it haunts his paintings, especially his many depictions of The Painter and his Model. It encapsulates the paradox of his art, for Picasso was the first artist to break the traditional picture apart, a leap many might call “abstract.” But even his most impenetrable Cubist paintings have a definite subject. He loathed pure abstraction. His art is always about something - a lover, a massacre.

Picasso knew that art is a kind of madness. It can obsess people, it can destroy them. He stands accused of sacrificing his family to his art. It worked: he painted to the end because he so ruthlessly made life serve art. That was his madness - “to see him as an egotist is a misunderstanding”, insists Baldassari. “He gave everything to his art, working every night. It was very lonely. This is my Picasso.”

When I visited the Picasso Museum in early September the collection had yet to be hung. Only a handful of Picassos were on display. Nevertheless the new President, Laurent Le Bon, decided to open the Hôtel Salé for a weekend. It felt like a mistake. Without many Picassos to look at, the only thing to examine was how the building has been transformed in these five years. What architectural coups have added to its lustre? After all, buildings do close for renewal, and with today’s computer design, advanced engineering and imaginative architects the results are often dazzling. There was nothing like that at the Picasso Museum. The exhibition space has supposedly doubled, and twice as much of the collection will be displayed. But as a regular visitor to the museum before it closed, I could not see any spectacular transformation. Something was wrong. Like the indecipherable painting in The Unknown Masterpiece, this long-awaited renewal seemed tragically misconceived. A kind of lunacy.

I returned to the museum this week for a preview of the opening, and it did look a lot better with Picassos in it. The masterpieces of his personal collection are all here, from his grotesque and entrancing 1901 portrait of the art critic Gustave Coquiot to a series of hilarious, filthy etchings he made in the 1960s, imagining his predecessor Degas visiting a very carnal brothel. When the 20-year-old Picasso first saw Montmartre he was visibly influenced by the sleazy down-to-earth art of Toulouse-Lautrec and the fierce colours of Van Gogh. But no previous Parisian avant-garde artist had ever delighted in ugliness and monstrosity in the way Picasso’s painting of Coquiot does. This readiness to be ugly and barbaric, and through that freedom to release new ways of seeing the world previously unimagined by western art before, is where Picasso is the true father of all that is dangerous in modern art.

This revolutionary shock becomes still more acute in a powerful display of his preparatory works for Les Demoiselles d’Avignon – paintings and drawings of twisted bodies and mask-like heads that he did in 1907 in his grotty studio in Montmartre. The natural light coming in through the large restored windows of the Hôtel Salé hits the rugged surfaces of Picasso’s paintings beautifully. The spectacular central staircase, with its classical caryatids and bunches of stone fruit, is a dreamlike and atmospheric way to go up to the second floor, where Picasso’s intense and strange surrealist art holds sway. Here is his nail-studded guitar like a witch’s fetish. Here are classicising and admiring – but maybe never quite loving – portraits of his first wife Olga, juxtaposed with vicious images of her as some demonic beast of rage.

Clever curators love unexpected juxtapositions of different styles and periods, and Baldassari is nothing if not a clever curator. But the supposed coups de theatre in her opening display are almost irritating, and confusing for all but Picasso specialists. A room near the beginning that brings together Picasso’s styles from the Blue Period to his old age is oddly dispiriting and diffusing, and hardly a good introduction for the general public, which would be better served by a simple chronological hang of the collection.

You are never allowed to forget, in the tall and remorselessly white rooms of the reborn museum, that you are in a palace. Picasso deserves one, to be sure, but the spacious walls, which are perfect for hanging his big pictures, sometimes leave the many smaller works in the collection looking lost. The bicycle Bull’s Head is hung high up on a soaring wall, in a way that utterly spoils its humour; the terrifying wartime Death’s Head is stranded on a vast white plinth, where it will certainly be noticed, but with its horror considerably diminished.

There is a loss of intimacy amid all the grandeur. Baldassari’s curation does not pull some magic lapin agile out of a hat to prove her critics wrong – and nor does it prove them right. It simply seems a bit overblown. Picasso does not need ostentation to make him look like a genius.

Picasso can do what few contemporary artists have achieved, to tear out your heart and twist your viscera

Anne Baldassari set out to put herself at the centre of Picasso’s legacy. Through books, exhibitions and her discoveries in the Picasso archives, she became part of what amounts to an aristocracy of Picasso scholarship and expertise. Her critics claim that she went too far – out of a “drunkenness of power”, as Vincent Noce told me in Paris. But if she was drunk on anything, it was Picasso. “This is no longer my museum,” she lamented when we met. Her successor, Le Bon, was not an easy man to interview, with the demeanour of a diplomat made of reflecting glass. But one remark summed up the contrast he wished to demonstrate with Baldassari: the Picasso Museum, he said, “does not belong to me”.

Pablo Picasso always did have a way of driving people mad. His first wife Olga is the model for the screaming women he painted with teeth bared at the sky, as their marriage fell apart. There is a visceral and obsessive quality to Picasso’s art. No other modern artist is as capable of sustaining such lifelong fascination. The wit of Duchamp and his successors may catch the pulse of our time, but Picasso can do what few contemporary artists have achieved, to tear out your heart and twist your viscera. He can take over your life. When I asked John Richardson, who is 90, if he felt he had dedicated his life to the right man, his response was immediate: “Oh god, yes!” Even Baldassari, after being sacked from the museum and returning in a lesser role, spoke with tireless energy about his work. And Claude Picasso has dedicated his life to championing the legacy of a father who spurned him.

The crisis at the Picasso Museum seems an image of our frayed relationship with Picasso himself. Revered, gossiped about and sold for ever grander prices, Picasso’s challenges to perception, sexual identity and political anger may be officially valued but their true meanings often seem too difficult, too genuinely modernist for today’s postmodern blagueurs. If the art of our time owes little to Picasso, that may stand as a critique of the art of our time. For what other artist since 1900, let alone 2000, has so truly engaged every side of human life, private and public, from the secrets of intimacy to the horrors of war? Only a handful of artists in history have ever shared his kind of genius. I felt exactly the same thing in this “new” Picasso Museum that I used to feel in the old one: awe. The abundance of Picasso’s imagination, the restlessness of his changes, the ever-reborn newness and the primal antiquity, are so self-evident in this collection that it cannot be ruined, or improved.

If the museum’s troubles ask a question about the vitality of Picasso for our time, they also answer it. The violence and turbulence, the emotion and engagement, that I encountered among the competing guardians of his legacy answers any question about his continuing power in our time. Picasso can still obsess. He can still ruin lives. A living artist? He remains a killing one. A devastating force.

• This article was amended on 20 October 2014. An earlier version wrongly referred to French patrimonie nationale rather than patrimoine national.

