Noel Le Graet has revealed Samir Nasri, Hatem Ben Arfa, Jeremy Menez and Yann M'Vila face disciplinary action for their behaviour at Euro 2012.
Nasri made the headlines for all the wrong reasons when he challenged a journalist to a fight after France's quarter-final exit at the hands of Spain, while the other three players were reportedly involved in a dressing-room bust-up after the Group D loss against Sweden.
"Four of our players will have to explain their actions to a disciplinary committee - Nasri, Ben Arfa, Menez and M'Vila," France Football Federation president Le Graet told reporters.
"By nature, I am not the type of person who likes to hand out punishments. It's not like I want any heads to roll. However, our players have to be sanctioned.
"I do not want them to come out of this as the victims because that's not the case here."
Le Graet discussed the potential arrival of Didier Deschamps as new national team coach, and insisted that the former Marseille boss has not rejected an offer from the FFF.
"I read this morning that Deschamps supposedly said no, but that's a mistake," Le Graet said.
"He wanted to be with his family first and didn't want to make a decision on this right now. We'll give him a few days time. The national team is still one of his dreams."
France are in the market for a new coach due to the departure of Laurent Blanc at the weekend and Deschamps is available after leaving Marseille on Monday.