Les Bleus remain second in Group I with 11 points from six games. They are currently level with leaders Spain, who will open up a three-point lead if they beat Finland later on Friday.
With two games left, France look as if they will have to settle for a second-place finish and attempt to qualify for the showpiece tournament in Brazil via the playoffs.
Karim Benzema was in the starting 11 but once again failed to find the back of the net and has now gone more than 20 hours without scoring for France.
Georgia stay second from bottom on five points.
France, who have not scored in their last five matches, next face Belarus away on Tuesday.
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- Karim Benzema