The world champions meet Argentina, the team that beat them in the 2004 Athens Games semi-finals on their way to the gold medal, in their final game in Group A which also includes Tunisia.
European champions Spain, who lost the 2008 Games final in Beijing to the U.S., are in Group B with hosts Britain, Australia, China and Brazil following Monday's draw at the Brazilian Olympic Committee headquarters.
"I think it's great, yes, really tough games to start with. Both teams will be wanting to play, get going, get the tournament started," Joanna Sutherland, London 2012 competition manager for basketball, said, referring to the U.S.-France game.
"I think we'll have some very competitive (men's and women's) tournaments in London. I'm very excited," she added.
Brazil, whose men's team return to the Games for the first time since 1996 in Atlanta, were sorry not to be drawn in the same group as the U.S. so avoiding a potential quarter-final clash.
"(Drawn in the same group) we wouldn't run the risk of facing the United States in the quarter-finals," said former Brazil team member Oscar, who played at his fifth and last Games in Atlanta.
"That already happened in 1996 and we lost," Oscar told reporters after the draw.
The three places still up for grabs in the 12-team tournament at the July 27-Aug. 12 Olympics will be decided at a qualifying tournament in Caracas from June 2-8.
The U.S. women's team, looking for their fifth consecutive gold medal, were drawn with China, Angola and three teams that will emerge from a qualifying tournament in Turkey to be played from June 25 to July 1.
The other group so far has Australia, runners-up at the last three Games, Russia, Britain and Brazil.