Scrum-half Dupont underwent surgery after suffering a fractured cheekbone in Thursday's victory over Namibia, putting hosts Les Bleus on the verge of the knock-out stages which take place on the weekend of October 14-15.
France's next game is against Italy on October 7 when a victory would guarantee top spot in Pool A and a last-eight tie, in all likelihood with World Cup holders South Africa. "The operation went well, he's resting.
He will be back training on Sunday," Servat told reporters. "I have no doubt about his ability to play the quarter-final," the former France hooker added.
Former World Rugby player of the year Dupont, 26, was helped off the pitch in last week's win over Namibia and has been at home since undergoing surgery on Friday.