The Serb, who has suffered a disjointed 2017 with poor form and injury, spent around two and a half hours toiling to get through.
He was broken at 4-4 in the final set but then reeled off three straight games to snatch victory in the second-round encounter.
“It was a very difficult match, with many changes of momentum,” the second seed, who won the Monte Carlo event in 2013 and 2015, said.
“It was very tiring for me, the first clay of the season.
“But this is the start of the Roland Garros build-up.”
Djokovic, who has won only one tournament so far this season - the Qatar Open at the start of January - twice recovered in the third set from breaks down.
He finally prevailed against Simon, ranked 32 in the world, when the Frenchman fired long on a return.
Djokovic last played on the ATP more than a month ago - though he did emerge to lead a Serbian Davis Cup win this month - and sat out the Miami Masters last month with an elbow injury.
Qualifier Adrian Mannarino stunned fellow Frenchman Jo-Wilfried Tsonga, eliminating the seventh seed 6-7 (3/7), 6-2, 6-3 as new father Tsonga played for the first time in more than a month.
Though he was knocked out, the loser goes away with positive thoughts: “You can always do things a bit better. But I think it was a good match, generally speaking,” Tsonga said.
“Now I’m going to practise again. I’ll try to come back and be better next time.
“I needed to win more points and be better with my serve, I got broken often today. I’m not used to being broken that much.”
Tommy Haas ignored his 39 years to post a 6-3, 6-2 defeat of Benoit Paire as the German’s 2017 goodbye tour continues.
Haas last played in Monte Carlo well over a decade ago: “I think 2004 was the last
time. Who did I lose to? Geez, I forgot.
“When you go out there and compete, you hope for the best - to try to play well and try to win.
“Any time that happens obviously in this stage for me, it’s a very nice feeling.”
In other first-round matches, French 11th seed Lucas Pouille beat Ryan Harrison 6-2, 6-4 while Gilles Muller stopped Spain’s Tommy Robredo 6-2, 6-2.
German Jan-Lennard Struff eliminated promising Norwegian wildcard Christian Ruud 6-4, 6-4.
Kvitova targets French Open comeback
Petra Kvitova is planning a surprise return at the French Open, six months after her left hand was badly injured in a knife attack, she said on Monday.
The two-time Wimbledon champion suffered severe injuries to her playing hand as she fought off a knife-wielding intruder at her home in the eastern Czech town of Prostejov in December.
Doctors had estimated that the Czech star, ranked 14 in the world, would not be able to return to competition before the second half of the year.
“My name will appear on the entry list for Roland Garros tomorrow,” Kvitova said of the May 28-June 11 tournament in a post on her Instagram account.
“As the entry deadline approached, I had made good progress in my recovery process and I want to give myself every last opportunity to be able to compete at one of my favourite events.
“This unfortunately does not mean necessarily that I will be ready to play in Paris, but that I’m doing everything possible to give myself the chance and keep a positive mindset.
“There remains a long road ahead but I wanted to share this update with you. Thanks for your continued support and I hope to see you soon.”