© Getty Images
The British number three has established himself inside the world's top 100 during 2016 and he could move inside the top 80 in the ATP standings after a 6-4 3-6 6-1 triumph over the experienced Frenchman.
Edmund broke Simon early in the opening set and although the former world number six broke back, Edmund struck again to move closer to the last 16.
The 21-year-old broke in the first game of the second set but Simon took six of the next eight games to set up a decider, which was delayed at 2-1 to Edmund due to rain.
When the two players returned, Edmund seized the initiative with two successive breaks before sealing his place in the second round on his third match point.