Paul Pogba, N'Golo Kante and Presnel Kimpembe -- three key players from the team that won the World Cup in Russia in 2018 -- were ruled out by injury before the team left for Qatar.
Coach Didier Deschamps must now juggle his options as his squad is reduced to 24 players.
Deschamps said in a statement: "Like all of the group, the players and the staff, I am extremely upset for Lucas.
"We are losing an important player. Lucas is a fighter and I have no doubt he'll do everything possible to get back to full fitness."
France captain Hugo Lloris said: "Honestly, it's starting to become a big deal.
"We sensed immediately it was serious," the Tottenham Hotspur goalkeeper added after the match.
"It's the latest blow but we have to continue moving forward. It's going to make us stronger."
France, bidding to become the first team to successfully defend the title since Brazil in 1962, had to come from behind after Craig Goodwin's ninth-minute opener for the Socceroos.
Olivier Giroud scored twice to equal Thierry Henry on France's all-time scoring list on 51 goals, with Adrien Rabiot and Kylian Mbappe also on the scoresheet.