After comfortably winning the first set against the French qualifier, Murray made some unforced errors in the second before breaking early in the third.
The British number one faces Frenchman Benoit Paire next as he begins his clay-court campaign before May's French Open.
British number two Aljaz Bedene plays Rafael Nadal in his second-round match.
Murray, 28, is also competing in the men's doubles, where he and partner Dom Inglot progressed to the second round by beating Pablo Cuevas and Marcel Granollers 6-3 6-4 on Monday.
The Scot and Englishman Inglot next play Edouard Roger-Vasselin of France and Serbia's Nenad Zimonjic.
