It was the second straight Olympic championship for the French, which overcame a loss in group play to 2008 silver medalist Iceland.
Michael Guigou scored five goals in helping France become the first repeat team handball champion in Olympic history. The sport has been contested in the Games since 1972.
Sweden won the silver medal for the fourth time and is still looking for its first Olympic crown.
The bronze medal went to Hungary, which defeated Croatia in the third-place game 26-23.
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