Between the wooded parkland of the Bois de Boulogne and the first lazy bend of the river Seine, just to the west of Paris, there is an "island" of millionaires. The leafy, silent streets of mansions and mansion flats are divided from the city by the Bois; they are separated from the towering La Défense office district by the river; and they are cut off from the bulk of Neuilly-sur-Seine, the richest town in France, by an eight-lane, urban motorway called the Avenue Charles de Gaulle.

Into this secretive enclave, there has intruded in the last couple of weeks a noisy public psychodrama of the kind that only French – or maybe American – public life could script. At the centre of the "island" is a squat, nicotine-coloured, 1930s mansion, which is the home of 87-year-old Liliane Bettencourt, the wealthiest woman in France and heiress to the L'Oréal cosmetics fortune.

Mme Bettencourt, a very private and allegedly very befuddled woman, has been the subject of a billion-euro family squabble for almost three years. In the last two weeks, however, the mother and daughter spat has exploded into a state scandal with the pyrotechnic brilliance of the Bastille Day fireworks that will illuminate the Eiffel Tower tonight.

Stroll five minutes to the south of Bettencourt's concrete mansion and you stumble on the still-grander house once occupied by the Duke and Duchess of Windsor. Stroll 10 minutes to the north and you plunge into the unpleasant roar of the Avenue Charles de Gaulle: the once-elegant, westward extension to the Champs Elysées, now the eastward extension of the A14 autoroute used by 200,000 cars a day.

Not everyone in Neuilly-sur-Seine is super rich. Halfway along this avenue is a comparatively modest flat where three half-Hungarian brothers were brought up in the 1960s by a courageous, abandoned, half-jewish French mother. The second of those sons rose to become a very youthful mayor of Neuilly and a youthful – in French terms – President of the Republic, Nicolas Sarkozy.

As the mayor of Neuilly, M Sarkozy came to know Mme Bettencourt very well. How well is a matter of dispute. Last week, it was alleged that the Bettencourt family illegally funded M Sarkozy's early political career with envelopes stuffed with cash. The President angrily denied the allegation on live television on Monday night – but that particular accusation had, in fact, already been withdrawn. And many other allegations, oddities and discrepancies remain.

Bastille Day is France's national commemoration of the capture of the infamous fortress-prison 221 years ago – but it will be celebrated in a more schizophrenic political mood this year: part revolutionary, part fearful, part depressed, part cynical, part excited that the August holidays are approaching. The traditional Elysée Palace garden party has been cancelled by M Sarkozy (as a concession to the economic crisis). The traditional Champs Elysée parade, a colourful demonstration of the power of the French state, from new rockets to ageing fire engines, will go ahead.

The French economy is stuttering rather than failing. The government has yet to impose the kind of painful spending cuts envisaged in Britain or Germany. France's traditional alliance with Germany within the EU has been undermined by divergent views on how to respond to the recession and how best to defend the euro. The country is divided by – but not entirely opposed to – the radical notion that French people should work beyond the age of 60.

On the surface, non-political France remains calm and even prosperous. Why, then, such a strange and febrile political mood?

Even by French standards, the summer of 2010 has been wonderfully rich in drama. Last month, the France football team was knocked out of the World Cup after briefly going on strike. The behaviour of the, mostly black, French players – brought up in the troubled multi-racial suburbs or "banlieues" of large French cities – provoked a short, nasty political debate. "You can take these kids out of the banlieues and pay them €8m a year but you can't take the banlieues out of the kids," several politicians suggested.

Some of the comments were made by politicians of the far right (which is undergoing an upheaval of its own as the "liberal" Marine Le Pen threatens to take over and modernise her daddy's family business). Other quasi-racist comments about the France team were made by senior members of M Sarkozy's ruling centre-right party, the Union Pour un Mouvement Populaire (UMP).

This summer has also seen the trial of the alleged €5bn rogue trader, Jerome Kerviel. His ambitious activities in 2007-08 occurred in La Défense, just across the river from Mme Bettencourt's mansion. La Défense is the biggest and the most lucrative office development in Europe: a kind of Manhattan-sur-Seine. Last year, it almost fell under the political leadership of a 23-year-old law student, who was – entirely coincidentally, the country was assured – President Sarkozy's younger son, Jean. Cue ironic pause.

For delinquency in the French suburbs – and a sense of entitlement and immunity on a mega scale – it seems you don't have to go to the crumbling, drug-haunted housing estates of Seine Saint Denis or Essonne. You can also visit the calm streets and glass skyscrapers of the "rich" banlieues, just west of Paris, also known as "Sarkoland".

The Bettencourt scandal is threatening to the President partly because of when it happened (at a time when ordinary French people are being asked to accept job losses and public-spending cuts). It is even more dangerous because of where it happened, in Sarkozy's own political and spiritual heartland.

The legal ins and outs of the affair may never be elucidated; and certainly not before the presidential election of 2012. But the political damage to M Sarkozy may already be irreparable.

President Sarkozy was elected in 2007 as as new kind of politician. He was not part of the Old France of old money and old values and its self-preserving (and self-serving) administrative-political élite. He was a partly foreign, anti-intellectual bling-bling product of a can-do New France of new money, enterprise, advertising, the media and the law. Unlike most other centre-right politicians, he had never been convincingly accused of corruptly financing his political career.

He promised to bring "rupture" from the old, self-satisfied, immobile France. He would reconcile France with enterprise and hard work and (yes) money. He would remove the hidden barriers to social advancement. He would preserve the best of France while preparing the country to compete successfully in the "real" world.

Three years on, Sarkozy's reform programme is a series of works in progress or abandoned construction sites. The recession, and his own mis-steps – especially the egregious Jean Sarkozy affair – have reduced his popularity and room for political manoeuvre. French people have the impression that the Sarkozy presidency, which was supposed to be all about them, has been all about him: his overweening son, his Rolex watches, his noisy divorce, his trophy wife and now his billionaire friends.

The Bettencourt affair has – rightly or wrongly – punctured Sarkozy's reputation for probity. Worse, it has suggested that he is not a new kind of French politician at all but another political inside-trader – or rogue trader – operating not to break down barriers but to serve the interests of his own coterie of friends and backers.

The affair has a wonderful bunch of characters who could be the cast of a satirical play: Moliere rewritten for the 21st century. There is Liliane, the lonely octogenarian billionairess, who has fallen under the spell of a gay society photographer, François-Marie Banier, aged 63. There is Françoise Bettencourt-Meyers, Liliane's highly intellectual daughter. There is Patrice de Maistre, the manager of Liliane's €14bn fortune and a pillar of French haut-bourgeois society. There is Eric Woerth, the stiff and dignified employment minister, ex-budget minister and chief fundraiser for M Sarkozy's political party, the UMP.

There is Liliane's ex-butler, Patrice Bonnefoy, who secretly taped many of her conversations between April 2009 and May 2010. There is her former accountant, Claire Thibaut, who like the butler, sympathised with the fears and suspicions of Liliane's daughters about the influence of the photographer friend, M Banier.

Three years ago, Françoise Bettencourt-Meyers brought a legal action accusing M Banier of abusing her mother's "weakness of mind". Over a period of years, Liliane Bettencourt had given M Banier cash, art masterpieces and life-insurance policies worth just under €1bn.

The affair became deeply political three weeks ago, when the butler's secret tapes were given to the police and leaked to the press. They suggested that President Sarkozy had tried to manipulate the justice system to block Françoise Bettencourt-Meyers' legal action. They suggested that Mme Bettencourt was systematically hiding part of her fortune abroad to fiddle her taxes. They suggested that M Woerth, then budget minister in charge of hunting tax evaders, but also the party fundraiser, had asked for a job for his wife, Florence, managing Mme Bettencourt's money.

The tapes revealed much, much more. They painted a compellingly unpleasant portrait of the atmosphere of hypocrisy and greed among Mme Bettencourt's friends and advisers. The photographer M Banier – a man who claims to abhor money, like much of bohemian-artistic France – emerges from the tapes as a money-obsessed bully. The financial adviser, M de Maistre, is seen to both detest and protect M Banier, while wheedling a large cash present out of Mme Bettencourt for the yacht "of my dreams".

The whole affair exploded into even higher (or lower) politics last week. Mme Bettencourt's former accountant, Claire Thibaut, gave a statement to investigators. She also gave an interview to a left-wing website, Mediapart. She was quoted as saying that she had helped to raise an illegal €150,000 cash payment from Mme Bettencourt to M Woerth for Sarkozy's campaign in the 2007 presidential election. She also said that M Sarkozy, as mayor of Neuilly, was often given envelopes stuffed with cash by Mme Bettencourt and her late husband, André.

Claire Thibaut has since repudiated the second allegation as a "romanticisation" on the part of the website. She still insists to police that €150,000 in illegal cash funds for the Sarkozy campaign were given to M Woerth.

Does this explain why President Sarkozy took Liliane Bettencourt's side against her daughter, despite the considerable evidence that the old lady was being bamboozled? Does this explain why Mme Bettencourt's elaborate tax evasions were not challenged by the French state?

In Monday night's live television interview, President Sarkozy furiously denied all charges and accused parts of the media and his political opponents of inventing "disgraceful" calumnies to derail his reform programme. He had never, he said, taken envelopes stuffed with cash from the Bettencourt family. He was not a "man of money". If he had been, he would never have chosen to be a politician. (This deliberately obfuscated the real point: the money was allegedly given to him to further his political career.)

M Sarkozy gave a polished, sober performance. Even his hair seemed to be greyer than usual, as if he had finally chosen to make himself look wise and presidential rather than hungry and youthful.

It was, however, a very soft interview which evaded many important questions. Sarkozy denied the allegations that the accountant had already withdrawn (ie, the envelopes stuffed with cash). He was never even asked about the €150,000 allegedly given to M Woerth for the 2007 Sarkozy campaign. He was not asked either if he had tried to block Mme Bettencourt's daughter's legal action.

It is too early to write off Sarkozy's chances in 2012. He may still be lucky in his opponents. The Socialists have a series of "nearly" candidates but no obvious strong contender. His great centre-right enemy, the former prime minister Dominique de Villepin, has started his own anti-Sarko party but tends to botch his projects.

Marine Le Pen is almost certain to succeed her father, Jean-Marie, as National Front leader in January. She plans to make the French far right more middle-class, less obsessed with the Second World War, more liberal on women's issues: in other words, more of a gallic UKIP than a gallic BNP. She may succeed. She may, on the other hand, tear apart the many, mutually hating tribes of the xenophobic French hard right.