Scotland lost for the first time in the Championship this season after victories over England and Wales, ending their hopes of a first Grand Slam since 1990.
Both sides played more than an hour with 14 men after Grant Gilchrist was shown a red card for the visitors and Mohamed Haouas for the hosts.
Tight-head prop Haouas started instead of the banned Uini Atonio as Fabien Galthie's home side played their first home game of the year six months out from hosting the Rugby World Cup after losing to Ireland two weeks ago.
Flanker Hamish Watson returned for Gregor Townsend's side after suffering concussion in November. Townsend's visitors, seeking just a second win in Paris in 24 years, decided to play with the strong wind in the first half but failed to make the most of the advantage early on.