Fashion is often seen as innately artificial or false: elaborate, expensive dress is an elaborate, expensive lie.
The Bourne Identity gets a lot of mileage out of this common equation of fashion and artificiality. The fashion house Les Classiques is, of course, not what it appears: it is supposedly just a store that sells expensive clothing, but it's actually an information relay for Carlos the assassin. Similarly, René Bergeron is supposedly a fashion designer, but he is (probably) really Carlos himself. And Jacqueline Lavier, the head of Les Classiques, is described and defined in terms of artificiality: she has "a face that age and cosmetics had rendered into a cold mask of itself" (14.68).
Fashion is, in fact, so fake and so artificial that at some points it starts to turn the whole novel into a false image of itself—or a parody. The scenes where Bourne spreads disinformation among the unsuspecting staff of Les Classiques are among the best in the book, with Bourne babbling at utterly clueless clerks and accountants about Carlos and espionage and death in the same rapid-fire tough-guy espionage shorthand that he uses for real throughout the novel. Take this, for example:
"We received word from Zurich and we want you to get it to your friend Lavier."
"Madame Jacqueline? My friend?
"We can't trust the phones."
"What phones? The word? What word?" (27.204-207)
The only difference is that here, Bourne's talking to fashionistas, not spies. The spy gabble is a ridiculous, artificial put-on.
Ludlum has a lot of fun playing with the spy genre, and we can see that in action here. The plot and prose of The Bourne Identity are always just on the verge of being a joke...and as Bourne terrorizes defenseless shop clerks with spy-chat mumbo jumbo, it tips right over that verge. Supposedly Bourne is infiltrating Les Classiques, but you could just as well say that Les Classiques is infiltrating Bourne. All those folds of fashion wrap luxuriously about him, and he acts like a babbling playacting goofball, spewing overblown dramatic nonsense to promote adrenaline rushes in clerks, accountants, and readers alike.