On a stifling Centre Court the 15th seed was pushed hard in the first set before 50th-ranked Edmund wilted in the heat and Monfils moved through 7-6(1) 6-4 6-4.
Monfils will face Frenchman Adrian Mannarino next as he bids to make the fourth round for the first time.
"I think I'm a good tennis player, but I've never done so good on grass. Never actually passed the third round at Wimbledon. Never had great result on grass," he said.
"One more match. I will see. I have to think about it."
Edmund's forehand, rated as one of the hardest in men's tennis, was a constant menace to Monfils in the first set and the British player had two break points in a titanic ninth game but could not convert either.
It proved a pivotal moment because Monfils went on to pocket the tiebreak with ease as Edmund buckled under the strain.
Edmund did manage to break back having fallen behind in the second set but Monfils always had the extra shot up his sleeve to wear down the 22-year-old.
"I played pretty solid, the first set was a crucial moment in the match and then I was cruising a bit," Monfils, who has reached the third round for the sixth time, told reporters.
Britain has four players in the third round of Wimbledon for the first time in 20 years with men's champion Andy Murray joined by Johanna Konta, Aljaz Bedene and Heather Watson.
Edmund said the success of the home players had not increased the pressure on his shoulders, although he was disappointed not to join his fellow Brits.
"In the past I have played on big courts and come off saying I didn't quite get my game going or only got going later on in the match, but I got going quite quickly," he said.
"A few shots in certain points or match situations just needed to be better on. I'm only 22 years old, I don't know all the answers. That's why it's a great thing to learn from."
(Reporting by Martyn Herman; editing by Clare Lovell)
Share
