The Serb, playing his first clay match of the year after recovering from an elbow injury, won 6-3 3-6 7-5.
The 29-year-old secured the first set before Simon saved four break points in the second to change the game's tempo.
Simon, ranked 32nd, had the chance to serve for the match but Djokovic fought through to reach the last 16.
Djokovic, a two-time champion in Monte Carlo, received a bye in the first round and appeared to feel some strain in his right elbow in a close final set against Simon.
He was broken by Simon after an error-strewn game but a series of lengthy rallies fell Djokovic's way, before the 32-year-old broke again.
Simon - who has not won a match since February - failed to serve out the match at 5-4, allowing Djokovic to find some rhythm and secure victory.
Elsewhere, France's Jo-Wilfried Tsonga was beaten by compatriot Adrian Mannarino 6-7 (3-7) 6-2 6-3.
World number one Andy Murray makes his return to the tour on Wednesday when he faces Luxembourger Gilles Muller, while Briton Kyle Edmund will play Spain's Rafael Nadal in the second round.