The scrum-half suffered the injury in France’s 96-0 thrashing of Namibia on Thursday night and is now in danger of missing the rest of the tournament.
Namibia captain Johan Deysel was sent off for the challenge that left Dupont’s tournament in doubt, and France’s home challenge plunged into chaos.
Les Bleus have now lost both their outstanding Toulouse half-backs, in Dupont and Romain Ntamack, who suffered knee ligament damage just before the tournament.
England defence coach Kevin Sinfield wished Dupont a speedy recovery, backing the world’s best player to return before the end of the competition.
“On behalf of everyone connected with England, we would like to pass on our best wishes to Antoine, and hopefully he’ll have a speedy recovery,” said Sinfield.
“I’m disappointed for the competition at this time, but I’ve no doubt he’ll be back. World-class players like that get themselves right very, very quickly. I’m sure he’s doing everything he can.
“With a facial fracture there will be a period of time, but we’ve seen players play before with facial fractures. So I suspect he will be back on his feet and back available very soon, and we wish him all the best.”
Harlequins and England scrum-half Danny Care hailed France counterpart Dupont as the world’s best player.
Care insisted that any rival would want to see the best players take the field in the World Cup, for the good of the competition.
“I echo what Kev said, we’re all sending him our best,” said Care. “And you want to see the best players at the World Cup, and Antoine is the best player at the World Cup so you want to see him back there in a French shirt.
“He’s tough and I’m sure if he’s able he’ll be back in a French shirt. He’s pretty special, so for the tournament I want to see the best players play, so we wish him a speedy recovery.”