Wendie Renard scored the winning goal from the spot 10 minutes from time.
The African champions finished third in the group with three points from three games.
The West Africans will now hope to pick a slot among the four best third-placed teams in the competition after the completion of other groups’ games.
Should they secure a berth in the knockout stages, the Super Falcons will face either Germany or Italy in the Round of 16.
The two sides struggled to create any clear cut chances in the first half as both goalkeepers remain untested.
The hosts, determined to maintain their winning run in the competition, piled pressure on the Super Falcons defence early in the second half but were let down by their profligacy in front of goal.
The Les Bleues were awarded a penalty in the 77th minute after Ngozi Ebere to have fouled Lee Sommer inside the box.
Ebere was sent off for the poor tackle which was awarded after the centre referee consulted VAR.
Renard initially missed the first spot kick but the referee ordered a replay as Chiamaka Nnadozie was adjudged to have moved her feet o out of the line.
The centre-back made no mistake the second time as she planted the ball into the net.
Asisat Oshoala limped out seven minutes before the end and was replaced by Anam Imo.
The Super Falcons with their numerical disadvantage were unable to mount a comeback succumbing their second defeat of the competition.