The world number two powered past the Frenchman at Roland Garros on Wednesday with a 6-1 6-4 6-2 victory.
Djokovic, 27, will now meet Croatian world number 26 Marin Cilic for a spot in round three.
"I managed to play some good tennis and [I am] already feeling like I'm improving my game as the tournament progresses," the Serbian told the ATP's official website.
"I managed to make him play an extra shot. I managed to stay solid from the baseline and I think that forced him to make a lot of unforced errors, which definitely helped me to win in straight sets."
Djokovic reached the semi-finals of last year's tournament in Paris before losing to eventual champion Rafael Nadal.