PARIS — At the tail end of Paris Fashion Week, at a party whose threshold was near impossible to breach, Rick Owens was chatting up Kris Van Assche, the Dior Homme designer, not far from Emmanuelle Alt, the editor of Paris Vogue. Chloë Sevigny was holding court in one corner.

The evening’s host, however, was most excited by the presence of teenage skateboarders in sweatsuit finery. Inside they mixed with fashion editors, while outside many more waited on quiet rue Barbette, desperate to get in.

Supreme, the New York skate line and 22-year-young beacon of cool, had arrived.

Its impresario, James Jebbia, 52, is not generally given to discussing the phenomenon he has presided over for two decades. “The less known the better,” he said in a rare interview. He is its founder and owner but not its designer, and prefers not to delve too deeply into the specifics of who is. The star of Supreme is Supreme.

“Ralph Lauren has Ralph Lauren, Tommy Hilfiger has Tommy Hilfiger,” Angelo Baque, Supreme’s brand director, explained. “We like for Supreme to be at the forefront when you think of Supreme. That’s the key, at least for me, for the brand to stay ageless and timeless.”

Supreme’s customary silence is in inverse proportion to the interest it generates, though understandable. Its hysterical appeal, and the siren song its red logo sings to its initiates, resist explanation. Its fans are exuberant and obsessive, poring over online message boards and lining up for hours, if necessary, to buy it. In July, one devotee, David Shapiro, will publish “Supremacist,” a semi-autobiographical novel about the spirit quest of a narrator named David to visit every Supreme store on earth. (Mr. Shapiro said in an interview that he had visited every store but Paris, and has planned a trip there in September.)

As a label, Supreme is hard to characterize precisely. It is skate-centric but not skate-exclusive (Mr. Jebbia himself does not now and never did skate regularly), with a durable provocative streak but otherwise catholic interests. It makes skate decks (many with blue-chip artists, like Jeff Koons and George Condo), clothes — including T-shirts, sweatshirts, jeans and outerwear — and accessories, as well as a variety of unlikely branded bric-a-brac, historically including fire extinguishers, toolboxes and ashtrays.

It collaborates widely with other brands (not only labels like Hanes for underwear and socks, but also Budweiser, the Yankees and Playboy). It orchestrates wheat-pasted ad campaigns starring inviolable icons well out of reach of most of its contemporaries, among them, Kate Moss, Lou Reed, Morrissey, Neil Young and Kermit the Frog. Its main models, though, are the young skaters of its own skate team.

Supreme has grown in stages. It began as a New York anti-establishment, one that has since 1994 kept Lafayette Street crisscrossed with skaters. Next came the big-in-Japan era, where, in 1998, the company opened the first three of its six stores in the country. In 2004, Supreme Los Angeles opened, and in 2011, the first European Supreme store opened in London. Paris is the latest addition. “It’s a natural progression, really,” Mr. Jebbia said.

The openings of Supreme shops are especially significant because, unlike most fashion companies, Supreme does not sell its wares at any stores but its own. (The sole exception to this rule is Dover Street Market, some of whose locations house Supreme shops.) Those who want Supreme must go to Supreme.

“Any brand in the world wants to make desirable product,” Mr. Jebbia said. “But we don’t shove it down people’s throats.”

In fact, the opposite is true. The limited distribution of Supreme’s collections, and the limited and unrepeated quantities in which they are produced, have made basically any piece a cult item, with a flourishing gray market of online resellers. Hourslong lines at nearly every Thursday-morning Supreme “drop” (when the stores are restocked with new product) are the norm.

Mr. Jebbia stiffens visibly discussing the lines and the perception that Supreme’s scarcity is manipulative or artificial.

“We don’t want people to think of Supreme as this hard-to-get, exclusive brand,” he said. “We’re a brand of the people.”

He is especially uneasy about the lines that have become a spectacle and a logistical obstacle. Websites send video crews to interview the waiting hopefuls as a kind of spectator sport. In rare cases, the line has been disruptive enough to be dispersed by the Police Department.

“It’s a good and a bad thing,” Mr. Jebbia said. “A lot of brands would like to have that problem.”

Mr. Jebbia sees Supreme as a youth brand, affordably priced (small accessories can go for as little as $18) and targeted at a customer who is 18 to 24 years old, for whom authenticity is paramount.

“What we don’t do is dumb anything down for kids,” Mr. Jebbia said.

But if Supreme’s lines are made up largely of younger fans, its appeal extends further. That the opening was set during Paris Fashion Week was not an accident. It has not escaped notice that the fashion community has enthusiastically embraced Supreme. Its T-shirts, sneakers and hats are low-key uniform staples for many editors at fashion weeks worldwide.

“I don’t look at what we do as fashion, but I wouldn’t say it’s not part of it, either,” Mr. Jebbia said. “When I see fashion people wearing it, I love it, too. Fashion people are picky.”

Even the picky veer into hagiography where Supreme is concerned.

“Supreme is the pinnacle of my generation in terms of a brand,” said Virgil Abloh, who works with Kanye West and shows his own collection, Off-White, in Paris. “James is a master visionary.”

Whether or not one considers Supreme’s own collections as fashion, the company regularly collaborates with fashion labels on capsule collections, the more unexpected the better. Nike, Levi’s and Comme des Garçons’ Shirt line are in regular rotation.

Adrian Joffe, the president of Comme des Garçons, is also the president of Dover Street Market, where in New York, Supreme is among the store’s top three best-selling brands.

Its space there is next to Gucci’s, which is “thrilled,” Mr. Joffe said, “to be next to Supreme.”

Now Supreme has its own permanent home in one of fashion’s most historic capitals, and though the label says that the Paris skate scene, not its fashion culture, is the reason, it may also be that Supreme, in its gruff heart, has a soft spot for fashion.

Paris, for the record, is home to another company often mentioned by Supreme admirers as a spiritual cousin, one that embraces heterodoxy with wide-ranging coherence: Chanel.

“I’m influenced a lot by Chanel and by what Karl Lagerfeld has done,” Mr. Jebbia said. “Oftentimes we get asked, ‘Why are you doing a fire extinguisher?’ I’m like, ‘Well, Chanel can.’”