It was a hard-fought match between the world no.2 and Simon, currently ranked at no.32.
After a sketchy start, in which both players lost their opening serves, Djokovic struggled to break through, and just managed to get the better of Simon to go 5-3 up and serve out the first set.
However, a determined Simon fought back after being broken early in the second set to go on to win 6-3.
Djokovic gave Simon an opportunity to finish the job quickly in the final set but he made a prompt comeback to shut down the Frenchman's subsequent serve.
At the 11th hour, Djokovic lost his serve to give Simon the advantage, but immediately broke back to take the third set to 5-5.
After holding his next serve comfortably, he narrowly avoided a tie-break by just edging past Simon to win his 11th match of the 12 between the two despite hitting 43 unforced errors.
Elsewhere in the second round of the tournament, David Goffin progressed after a 7-5 6-1 win over Nicolas Almagro, and Pablo Cuevas beat Joao Sousa 6-3 6-3.
Meanwhile Jo-Wilfried Tsonga made a surprise early exit after he was beaten 6-7 (3-7) 6-2 6-3 by Adrian Mannarino.
Read the original article on Eurosport: Djokovic overcomes stubborn Gilles Simon to progress in Monte Carlo