Nice pressured early on, with Jeremy Pied coming close to giving the home side the lead after 12 minutes.
Loic Poujol had Sochaux's first meaningful effort of the game on 18 minutes, though the strike went just wide of the post.
After 33 minutes, Mahamane Traore got up above the defenders to head towards goal, but his effort was just off target.
Dario Cvitanich drove forward two minutes later, but his strike went wide of the mark.
Traore gave the home side the lead after 51 minutes, finishing well to make it 1-0.
Nice then doubled their lead on 59 minutes through Didier Digard as they began to look much more comfortable.
Cvitanich extended Nice's lead on 84 minutes to effectively confirm all three points for the home side.
Giovanni Sio had a chance to grab a late consolation for the away side, but he put his effort wide.