A warm spring evening in Paris and the staff of Saint Laurent and their friends are having a drink. An hour ago, the brand's creative director Hedi Slimane unveiled his second womenswear collection at the Grand Palais. It was a multimedia extravaganza with a booklet of artwork by Theodora Allen given away as an invitation, and a commissioned soundtrack by psychedelic punks Thee Oh Sees played at pulverising volume. As well as designing the set, Slimane styled the show, just as he will shoot the ad campaign that follows, starring Cara Delevingne and Zachary Cole Smith from the band DIIV.

A model walks the runway during Saint Laurent autumn/winter 2013 show. Photograph: Victor Virgile/Gamma-Rapho via Getty Images

Slimane mingles in a black velvet jacket, chatting to his team, models from the show including Lily McMenamy, and long-term musician pals like Thomas Mars from Phoenix. Before he leaves at 10pm, someone suggests that, since they are still bigging up the ladylike look, the fashion press may not go a bundle on the grungy baby-doll dresses, plaid shirts and biker boots that Slimane sent down the catwalk. Overnight, reaction spreads across Twitter. Fans of Slimane's work, like Courtney Love, acclaim the show as genius; but others see it as an insult, outraged at what they perceive as Slimane's disrespect to the memory of Yves Saint Laurent.

Slimane's tenure at Saint Laurent has made him the most talked-about – and controversial – designer in the world. As soon as he was appointed in March 2012, he made modifications with a speed that left some commentators reeling. He changed the logo, moved the design studio from Paris to Los Angeles and started to refurbish the stores, decisions that were viewed with suspicion. Then his first two collections divided opinion, with an unlikely coalition including Anna Wintour, Kate Moss and Lady Gaga (who within days of the show wore an outfit from the S/S 2013 collection to meet Julian Assange at the Ecuadorian embassy) in favour, but some critics vociferously against.

It's a drama I've watched unfold with interest. I've known Slimane for nine years, a friendship which started when he was creative director at Dior Homme. He sent a book of his rock gig photography called Stage to NME, where I was deputy editor. We met and hit it off. We've been to clubs, gigs and pubs for fun, but also on a project called Rock Diary, a V magazine series, exhibition and book on the explosion of guitar bands in the mid-00s.

David Furnish, Kate Moss, Pete Doherty and Hedi Slimane at the Dior Men's spring/summer collection in 2006. Photograph: GoffINF.com/Angeli

The Hedi I know is low-key, funny and attitude-free. He combines a laser-like focus with an openness and enthusiasm for the chaotic and unpredictable – after all, this is a man who made a book about Pete Doherty while working at Christian Dior. The skinny jeans and suits he designed at Dior Homme, where he worked until 2007, changed the way a generation of men dressed. His talent was recognised by Yves himself; in 2001, the reclusive designer led the standing ovation at Slimane's first Dior Homme show.

Slimane does not talk to the press after shows, nor does he provide notes explaining his references. He's given one interview (to American Vogue this month) since he started at Saint Laurent. But he and his team did agree to discuss with me the collections and details of the reform programme that he's implementing at the house. The minutiae of his plans are thrilling to anyone who's a fashion nerd, but what is particularly fascinating is how all of Hedi's work – reported by naysayers as disrespectful, egotistical – was actually inspired by Yves Saint Laurent himself.

The two womenswear collections have received the most critical attention. The first, S/S 2013, intended to reposition Saint Laurent at the intersection of youth culture, high fashion and art. The A/W 2013 show was inspired by one of Yves's most significant collections – the 1940s-inspired clothes shown in January 1971, called the Libération de Paris. Its references to the Nazi occupation of France, together with deliberate camp that nodded to drag queens at Warhol's Factory and riots at the Stonewall Inn in New York, outraged the press. The International Herald Tribune described it as "suicidal", while Le Figaro accused him of playing "un long gag" – both charges levelled at Slimane 42 years later.

Yves's romantic and business partner Pierre Bergé and muse Betty Catroux, both of whom have sat front row at Slimane's shows, recognise that while the grunge may have épaté la bourgeoisie, it was consistent with Yves's principles: to question the nature of luxury, and to collide street fashion with the painstaking techniques of couture. In 1960, when 24-year-old Yves worked for Dior, he unveiled a couture collection inspired by beatniks in Saint-Germain jazz clubs, he showed that he wanted to dress his generation. For Slimane the intent is the same.

Saint Laurent Men campaign for spring/summer 2013. Photograph: Hedi Slimane/Saint Laurent

Slimane's reform is a wholesale restoration project. The brand was founded in 1961 as an haute couture house; five years later Yves and Bergé revolutionised the fashion industry with the first ready-to-wear line, Saint Laurent Rive Gauche. What followed was an epic of high finance, addiction and drama, as Yves Saint Laurent became an international fashion brand built on the talent of a uniquely talented but troubled man. Yves retired in 2002 and died six years later. Slimane had a stint at the house from 1997-2000 as menswear designer, and now he has returned as creative director he is determined to reassert its core values.

It's surprising that Slimane's logo – Saint Laurent Paris in Helvetica type – was regarded as so iconoclastic. He was berated for "dropping the Yves", but in fact the logo dates from 1966. It was used on Yves's ready-to-wear line and the Rive Gauche shop front. The famous YSL logo by Cassandre hasn't been junked. It appears on clothes and on giant banners outside the Grand Palais for the shows. Though it got lost in the general press uproar, Slimane's intention was to reassert ready-to-wear's identity from its couture sibling.

The references to Yves's history don't stop there. Slimane has introduced black tresse ouverte grosgrain ribbons, black boxes with a grain-de-poudre texture, and contrast of black matt and gloss on the label's bags and boxes. These are inspired by the label's legendary tuxedo, le smoking, while the embossed rectangles on the packaging are modelled on art deco panelling in Yves's rue de Babylone home.

As for the studio's relocation to LA, Bergé was unfazed, telling Women's Wear Daily: "The creative studio is in a designer's head. Hedi should be left to do fashion in a city he likes." Yves himself never designed in Paris, sketching at his house in Morocco, away from the pressures of the industry. Being in LA allows Slimane to work with bands like the Garden, who star in his menswear campaign.

The Saint Laurent studio in LA is a white cube, much like a large photo studio, with a team of between five and 10 people assisting Slimane – one might concentrate on womenswear, another on the cruise collection. The studio is the label's brain, where the design and imagery is created, but the craft happens in Paris, following strict couture traditions.

The restructuring of the couture ateliers have been the least visible but most significant element of the reform. When Slimane worked at the house in the 90s, it had a menswear atelier established by Yves in the 60s. At the beginning of the 00s this closed, leaving the house without tailoring specialists – astonishing given that Saint Laurent is home of le smoking. As Lauren Bacall put it in 1968 at the opening of the New York branch of Saint Laurent Rive Gauche, while wearing a black jumpsuit, "If it's pants, its Yves"; Helmut Newton's photograph of a woman on a street, smoking in a tuxedo, is part of the label's iconography.

Drawing on Saint Laurent's tailoring traditions and his own expertise, Slimane created a new atelier. It's essentially unisex: the women's suits are simply men's in smaller sizes. Slimane changed 90% of the production and new specifications were introduced – from lining (silk) to number of stitches per centimetre. "The idea is that if you're a woman and you need a men's suit, it has to be Saint Laurent, because tailoring is Saint Laurent, period," says an insider.

Slimane is famous for his ultra-slim proportions, but his clothes are surprisingly wearable due to the atelier's workers' ability to scale up size without ruining proportions. Some writers who have disliked the aggressive styling of the shows find that they love the clothes on the shop rail. Some of the baby-doll dresses were couture pieces, blending the cultures of the salon and the mosh pit.

One new element that feels very Slimane is the Music Project, in which musicians style themselves in their favourite Saint Laurent clothes from any season and are photographed by him. Kim Gordon, Daft Punk and Courtney Love have taken part, as have Ariel Pink and Marilyn Manson – who chose the same leather jacket.

This flood of images, often disseminated via social media before it appears in print, is intended to make Saint Laurent a dynamic presence. Its association with musicians plays to Saint Laurent heritage, too. In the 60s and 70s, bands went to Rive Gauche for stagewear; Mick and Bianca Jagger wed in matching white tuxedos (Bianca's from the notorious 40s collection). Yves's muses were party girls like Catroux and Loulou de la Falaise. Slimane's party girls are women like Sky Ferreira and Grimes, but the joie de vivre, sometimes undercut with sadness, is the same.

The most significant part of the project involves bricks and mortar. First the stores are being refitted. The flagship in Paris's avenue Montaigne is now a French modernist palace of marble and concrete with jewellery displayed in art deco mirrored vitrines; a similarly elegant downtown New York space opened in June and LA is next, with London's Sloane Street store opening in early 2014.

Hedi Slimane, 2012. Photograph: Getty Images

Saint Laurent has also acquired Hôtel de Sénecterre, a 17th-century mansion. Situated at 24 rue de l'Université, it puts Saint Laurent at the heart of the Left Bank, the brand's spiritual home. Not only did Yves and Bergé live and open their first store there, but the area's values infuse the spirit of the brand – Yves's A/W 1968 collection, full of duffle coats and fringed jackets, was dedicated to the student rioters.

For the first time since the company was sold to the Gucci group (now Kering) in 1999, the Hôtel de Sénecterre gives Yves Saint Laurent a public address. This is crucial to Parisians, who refer to fashion houses by location (rue Cambon for Chanel, avenue Montaigne for Dior).

Currently being restored to its 17th-century glory, Hôtel de Sénecterre will house a couture atelier and a salon. The intimation is that a couture wardrobe could be relaunched at Saint Laurent. Though Slimane has not confirmed this, it's a fascinating proposition. Saint Laurent will be a place connected to the fizzing energy of youth culture, dress its leading lights, but will also be rooted in centuries-old tradition. Should the collection happen, the name on the label will be Yves Saint Laurent, just as it was in the late designer's heyday. A fitting tribute from Slimane to Yves.