The match marked the return of the United States to the World Cup since it lost to North Korea in extra time of the 2008 final.
The American effort was hampered by being forced to replace center back Mandy Freeman - who was hit in the face - with Lizzy Raben in the 13th minute, the earliest substitution in tournament history.
Raben was critical in thwarting a pair of consecutive chances by Kadidiatou Diani in the 41st minute, blocking the first chance by the Frenchwoman, who put the rebound wide.
Campbell also denied Diani, twice diving to make stops, and also saving a Lea Declercq free kick.
The United States had only one shot on goal, Toni Payne's effort off a feed from Summer Green that was thwarted by French goalkeeper Romaine Bruneau, who raced off her line.
The result left both the Americans and French in second place in Group B, two points behind North Korea which routed Gambia 11-0 on Saturday.
The United States next plays against the African side on Tuesday.