Finland overtook the group lead from the Americans with a 7-2 win over Austria, but has a game more played, meaning the U.S. can clinch the top seed for the quarterfinals if it wins its last two round-robin matches against Germany and Slovakia.
"It would be great to finish No. 1, it would show we have accomplished something, but we have two tough games left," U.S. head coach Joe Sacco said.
Stephen Gionta and Bobby Butler gave the Americans a 2-0 lead in the first period, and captain Paul Stastny and David Moss added goals in the third.
"I try to be consistent with the lines, not shuffle around much," Sacco said. "I'd like to count on guys to take pressure off other lines. Like when Bobby Butler scored a big goal at the end of the first period on a nice play by Drew (LeBlanc)."
Kevin Hecquefeuille made it 2-1 for France in the second period and Yorick Treille added a late goal.
American goaltender Ben Bishop had 15 saves, including a couple of key stops to keep his team ahead early in the third. Cristobal Huet had 32 saves for France.
In Stockholm, group leader Switzerland beat Denmark 4-1, and Sweden shut out last-place Slovenia 2-0.
Finland took a 3-0 lead against Austria over the first two periods. The Austrians scored two quick goals at the start of the third before Finland responded with four unanswered goals. Veli-Matti Savinainen had two goals for Finland while Petri Kontiola scored his sixth of the tournament.
In Stockholm, Switzerland got goals from Luca Cunti, Ryan Gardner, Reto Suri and Nino Niederreiter.
The Swiss haveo 14 points from five games, one ahead of Canada.
Sweden outshot Slovenia 40-21 but had to be content with goals by Gabriel Landeskog in the first period and Fredrik Pettersson on a power play in the third. Twins Daniel and Henrik Sedin have yet to join up with the team after the Vancouver Canucks were knocked out of the NHL playoffs.