By Simon Evans

LYON, France (Reuters) - As the United States began celebrating their World Cup win over the Netherlands on Sunday, FIFA president Gianni Infantino strode out on to the field with French president Emmanuel Macron.

The boos ringing out from the stands at the Groupama Arena were initially directed at Macron, a reflection of the current political mood in France, but it wasn't long before Infantino also got a reminder of the issues facing him.

"Equal pay, equal pay!" chanted the U.S fans behind the goal and while Infantino could perhaps tell himself that those words related to the U.S team's long-running dispute over compensation with their own national federation, the FIFA president is surely under no illusion that the days when the women's game was glad just to have opportunities to perform are long over.

On Friday he announced that, as part of renewed investment in the women's game, $1 billion (up from $0.5bn) would be spent over the next four-year cycle. The prize money for the next women's World Cup would also be doubled from $30 million to $60 million.

But just 24 hours later United States captain Megan Rapinoe used a FIFA-organized press conference to point out how the men would still receive much more in prize money - $440 million - at their next World Cup in 2022.

Rapinoe also took aim at the governing body over the scheduling of two men's continental competition finals on the same day as the women's match and suggested that FIFA didn't "care" about the women's game and weren't showing enough "respect".

Regardless of the merits of those arguments, the fact that a leading player like Rapinoe, one of the stars of this tournament, was willing to criticize FIFA on the day before the showcase game was a clear sign that things have changed.

FIFA has been justifiably proud of the large World Cup attendances, with stadia over 75 percent full throughout and a crowd of 57,900 watching the final in Lyon.

Even more impressive have been the record-smashing television ratings. In the past, the United States has enjoyed huge numbers for the tournament, given the success of their team, but the increasing numbers for countries such as England, France and Italy show the appetite for top women's games is now established in Western Europe.

Countries with a strong tradition in the men's game but who have been slow off the mark with women's football, such as Spain and Italy, have shown signs of improvement -- both in the quality of their football and the level of interest generated by their national sides.

And with Europe's big clubs, such as Manchester United and Real Madrid, creating top-level teams to compete with the early adopters, such as Arsenal and Olympique Lyon, the finances flowing into the game at club-level are spiking.

MOVING TO THE NEXT STEP

It is within that context that the debate over the future of women's football will take place.

"I think everyone is ready for this conversation and to move to the next step. I think we're done with 'are we worth it?'" said Rapinoe, her winner's medal around her neck.

"Should we have equal pay? Are the markets the same? Everyone's done with that, fans done with that, players done with that, you know, along with the sponsors.

"Let's get to the next point of what's next?"

Rapinoe urged a focus on spreading the game further internationally -- a goal shared by some of the champions for women's soccer within FIFA, such as Sarai Bareman, the organization's Chief Women's Football Officer.

Bareman is keen to see money from FIFA ring-fenced for women's development programs in developing countries and areas where the sport has yet to flourish, and she has been forthright in pushing national federations to fully embrace the women's game.

The prize money issue won't go away -- nor will national battles, such as the struggle for better compensation and conditions for the world champions -- but Rapioe is surely right that the agenda has moved on.

"We put on the most incredible show that you could ever ask for," said the American, who at 34 has likely played her last World Cup.

"We can't do anything more to impress more, to be better ambassadors, to take on more, to play better... It's time to move that conversation forward to the next step."

It would surely be no surprise if Rapinoe, such a prominent voice in the women's game, plays a big part in that debate.

(Reporting by Simon Evans; editing by Tony Lawrence)