Les Bleus laboured to a 2-1 win against 1995 champions Norway on Wednesday after thrashing South Korea in the tournament's opening game last Friday.
The U.S. are widely expected to also progress top of their group after claiming a record 13-0 victory against Thailand. The draw shows that Group A and Group F winners, if they win their last-16 match, will face each other for a place in the last four on June 28 in Paris.
"We saw them against Thailand. Very strong team, we know that. But it's still far away and we feel that the fans are behind us, they're pushing us. We'll see," said defender Marion Torrent.
The prospect of facing the three-time world champions does not seem to worry coach Corinne Diacre, who does not want to see past the June 17 match against African champions Nigeria in Rennes.
"I take it game by game. We want a perfect record," she said.
"We are still underdogs (in the competition). We're not favourites at all."
France, however, beat the U.S. 3-1 in their last encounter in January and at home, the support for Les Bleus has been fulsome.
They were 34,872 fans at the Allianz Riviera for an official capacity of 35 ,624 on Wednesday and the Parc des Princes was sold out for the opener last week.
The French team have also attracted record viewers, with 9.4 million watching on TF1 on Wednesday after 9.83 million tuned in for the opening game.
With others watching the games on Canal Plus, more than 10 million watched both France matches.
(Reporting by Julien Pretot; Editing by Christian Radnedge)
