For many in women’s soccer, the reference point in United States sports is something else entirely: both Emma Hayes, the coach of Chelsea, the team Lyon narrowly beat in this year’s Champions League semifinals, and Phil Neville, the England national team coach, call Lyon the Harlem Globetrotters. This is a club that does not lose. It is the most dominant — and possibly the best — sports team on the planet.

Much of that, of course, is down to the quality of player at its disposal, to Aulas’s determination since he launched the women’s team in 2004 to acquire the sport’s brightest stars. The squad, now, contains not only Ada Hegerberg, the inaugural winner of the women’s Ballon d’Or as the world’s best player, but the backbone of France’s team for this year’s World Cup, Dzsenifer Marozsán, the captain of Germany, and Saki Kumagai, the captain of Japan. Its list of alumnae is, if anything, even more impressive: Camille Abily, Louisa Nécib, Hope Solo, Megan Rapinoe, Alex Morgan.

It has created a virtuous circle: Players want to join not just because it is acknowledgment of their status, but because they know that training at — never mind playing for — Lyon offers a fast track to self-improvement.

“Alex went to France to grow as a footballer and challenge herself every day,” said Dan Levy, Morgan’s agent. “She did that by playing with many of the best players in the world each day. Winning championships was wonderful, the training facilities were first class, but the secret of their success is that — by accumulating so many amazing players — they have created the perfect training environment.”

But just as significant is the club’s culture. Bronze confesses to being a little “star-struck” on her first day, walking into a dressing room populated by so many famous faces — “people I knew straightaway just by their surnames” — but soon found there was no concrete hierarchy to be navigated, no deference expected. “They all came over to introduce themselves,” she said. “They are the most humble group of people I have ever met.”

The club, though, does not treat them like that. When Lyon’s players departed for Budapest on Friday morning, they were driven to the airport and straight onto the tarmac, where they boarded a chartered jet. A second plane had been commissioned to carry family members and partners to the match. When they landed, the Lyon team bus — which set off, overland, earlier this week — was there to meet them.