And it is there in the way this team uses its fame, its primacy, its platform to promote the causes that energize it, from L.G.B.T.Q. rights to equal pay for equal work. A squad that lacks a sense of self does not sue its own federation on the eve of a tournament. This is not a team afraid of its own power, a team unwilling to speak its mind, a team unsure of its place or its role.

Exactly the opposite, in fact. What characterizes this incarnation of the United States is a coolness that folds easily into ruthlessness. Jürgen Klopp, the Liverpool manager, coined a phrase for his team, winners of this season’s Champions League: “mentality monsters,” a side that could not countenance the idea of being beaten. It fits the United States like a glove.

The potential matchup of France and the U.S. in the quarterfinals was spotted by most as soon as the draw was made late last year: the host against the holder, the two favorites for the tournament, the two best teams in the world. As soon as the game was confirmed, Rapinoe had said she hoped it would be a “circus.” She said she wanted it to be something else, too — a profanity-laced word intended to convey that it would be something bubbling and boiling and chaotic and sprawling, an epic that fit no easy narrative.

It was all of those things, in the end; Rapinoe was granted her wish. The United States scored early, but France did not wilt, the rhythm of the game beating ever faster, its pulse racing and its blood coursing. The crowd had started out waving tricolors and Stars and Stripes, trading chants, trading languages. As the game wore on, as the tension grew, the noise became more fevered, more feral. Night set in; the lights blazed.

But amid all of that, the United States players somehow stood apart. They were at the circus, they were enjoying the circus, but they were not part of the circus. Rapinoe’s second goal illustrated it as well as anything. Her team had missed a slew of chances right at the start of the second half. The reprieves clearly inspired the French, redoubling their belief that all was not lost.