Simon served for the match at 5-4 in the third set but world number two Djokovic broke back before breaking again to secure victory in just over two and a half hours.
Djokovic, winner of the event in 2013 and 2015, forced 16 break points in the match and took six of them, but lost five of the six he faced on his own serve.
But he made the breaks when they mattered and clinched victory from his first match point to progress 6-3 3-6 7-5.
Jo-Wilfried Tsonga is out of the competition after losing to fellow Frenchman Adrian Mannarino.
Seventh seed Tsonga won the first set on a tie-break but the world number 56 battled back to win 6-7 (3/7) 6-2 6-3 to reach the third round.
David Goffin is safely into the third round after beating Spain's Nicolas Almagro. The 10th seed sailed through 7-5 6-1 in 70 minutes.
In the day's first-round action, 11th seed Lucas Pouille beat Ryan Harrison 6-2 6-4 while Gilles Muller dropped only four games as he beat Tommy Robredo to set up a clash with world number one Andy Murray.
Croatian Borna Coric, who won his first ATP Tour title on Sunday, suffered a 7-6 (7/3) 3-6 6-3 defeat to Jeremy Chardy in a match that lasted two hours 42 minutes.
France's world number 40, Benoit Paire, suffered a 6-2 6-3 defeat to veteran Tommy Haas, now 655th in the rankings, while 16th seed Pablo Cuevas eased past Joao Sousa 6-3 6-3.
Another couple of French players suffered early exits as Nicolas Mahut lost in straight sets to Karen Khachanov and Pierre-Hugues Herbert was beaten 3-6 6-2 6-1 by Carlos Berlocq.
Also reaching the second round on Tuesday were Jiri Vesely, Paolo Lorenzi, Feliciano Lopez, Robin Haase and Jan-Lennard Struff.
