REIMS, France — By Saturday, the Women’s World Cup will have been winnowed from 24 teams to four. And either France, the host nation, or the United States, the tournament’s three-time and defending champion, will be gone.

That’s the inevitable outcome after the U.S. women brawled to a 2-1 victory over Spain on Monday in the medieval town of Reims, playing their ugliest but toughest soccer yet to clinch a spot in the quarterfinals.

Their reward: a date with France, whose players weathered their own trial the night before to vanquish Brazil by the same score.

In so many respects, this all-too-soon clash is a pity. It’s a borderline sporting offense that the tournament’s two best teams and top ticket-sellers, whose players have combined to score 30 goals and concede just three, must square off in the quarterfinals.

In the view of U.S. striker Megan Rapinoe, however, it’s cause for celebration.

After burying two penalty kicks against Spain to avert what would have been the greatest upset in the history of U.S. women’s soccer, Rapinoe was positively beside herself over the prospect of taking on France in a quarterfinal Friday at 45,000-seat Parc des Princes in Paris.

If her steely performance against Spanish goalkeeper Sandra Panos didn’t make it clear, Rapinoe is a big-game player. On her calendar, there’s never a bad day to compete against the best, on the biggest stage, with as many fans as possible watching.

“Hopefully, it’s a spectacle! An absolute media circus! I hope it’s huge and crazy, because that’s what it should be,” Rapinoe said, her white-blond hair tinted pink for the World Cup’s round of 16, when asked whether she lamented the meeting with France arriving in the quarterfinals.

“This is the best game. This is what everybody wanted,” she continued. “We want it. Seems like they’re up for it. . . . These are the biggest games, that you kind of dream about as a kid.”

With each round of this World Cup, there has been an air of inevitability about a France-U.S. quarterfinal.

From the moment France opened the tournament June 7 with a 4-0 rout of South Korea, both Les Bleues and the Americans have done their part.

Coaches Jill Ellis and Corinne Diacre have deployed the depth and mixture of youth and experience on their prodigiously talented rosters. And the athletes have delivered on the field — Elllis’s Americans with a display of offensive firepower that went on a walkabout Monday against Spain, forcing the squad to win with grit; and Diacre’s France with a master class in what a truly balanced soccer team looks like. France has no discernible weak link, only competence and cohesion binding its defensive backfield to midfield and, in turn, to the forwards up front.

Friday’s quarterfinal promises to be a study in contrast.

It also promises to be a raucous rebuttal to FIFA, the sport’s international governing body, and the national soccer federations that defend their grudging, parsimonious funding of the women’s game by arguing that women’s soccer doesn’t generate revenue and never will.

While several matches in this World Cup have had glaring numbers of empty seats, a crowd of 45,261 jammed Parc des Princes for France’s opener against South Korea.

When the U.S. women took on Chile the following week, attendance swelled further, to 45,594.

FIFA allocated a majority of available World Cup tickets to the French people, who accounted for 460,748 in sales, according to the Associated Press. After the French, Americans accounted for more ticket purchases — 130,905 — than the rest of the world combined.

So expect revenue to be generated Friday night in Paris, where fans of the red, white and-blue and France’s blue, white and red will paint their faces, wear crazy hats, drape themselves in flags, sing “The Star-Spangled Banner” and “La Marseillaise” and chant, scream and cheer.

Among them will be the three siblings and parents of U.S. midfielder Rose Lavelle, who has provided a terrific spark in her World Cup debut. It was a Spaniard’s kick to Lavelle’s lower right leg that drew the penalty that summoned Rapinoe for the second of her penalty kicks, in the 75th minute of a match that had been deadlocked at 1 since the ninth.

“Sometimes you have to win ugly and you have to dig deep,” Lavelle said, arguing that Monday’s struggles with Spain would help the U.S. team going forward. “That whole game was all about grit and how much we could handle when things weren’t going our way. I think it honestly is a big character-builder for us.”

The night before, Lavelle had watched France’s round-of-16 clash with Brazil. And she was struck Monday by this new parallel between the French and American teams, both forced to summon their best to clear the first test of the tournament’s knockout rounds.

“They’re a great team — technical and fast,” Lavelle said of France, relishing the matchup, particularly after the teams’ most recent meeting: a January friendly in Le Havre, where Les Bleues handed the Americans a 3-1 loss that was more lopsided than the score indicated. The U.S. squad that Ellis fielded then lacked Rapinoe, Tobin Heath and Julie Ertz.

Nonetheless, there’s little reason to expect France will be intimidated by the Americans when they meet again Friday.

“It’s going to be a great matchup,” Lavelle said. “It could easily be a finals game. No disrespect to any other team, but it’s two very strong teams with a lot of very good players.”