The 21-year-old, from Beverley, outplayed the experienced Frenchman to take a 6-4 3-6 6-1 win the in the first round of the Aegon Championships.
World No 18 Simon is the highest ranked opponent Edmund has beaten, trumping his previous best victory over world No 43 Martin Klizan at Dohar in January.
“It was definitely a great win,” said world No. 85 Edmund.
“On paper it’s my best, but it’s tough to say if it’s the best win of my career.
“When you look at your best you look at how you play and the situations and the opponents and everything together.
“I don’t know if it was ‘the’ best win, but I’d definitely say it’s one of the best wins of my career. That’s for sure.”
Edmund moves into the second round at the Aegon Championships, where he will face another Frenchman, Paul-Henri Mathieu, who beat Dan Evans 7-6 (10/8) 6-7 (6/8) 6-3 to end hopes of an all-British clash.
The British number four spurned three set points in the opening set but battled back, only for Mathieu to grab a decisive break in the decider.
“I don’t know a lot [about Mathieu], to be honest,” admitted Edmund.
“I practiced with him two or three years ago at Eastbourne. That’s it, really. The good thing is Dan played him today, so there is some information there.
“Obviously he’s done well to tough out three sets against Dan.
“I’ve been hitting with Dan, he’s been playing well. So I’m sure Mathieu has been playing well too.
“It’s just another match, I’ve got to go out there. I’ve got a match under my belt now, so I will learn from that and try and be better for the next round.”
Top seed Andy Murray will face fellow Briton Aljaz Bedene for a first time in round two on Thursday.