Samir Nasri, Hatem Ben Arfa, Jeremy Menez and Yann M'Vila have all been accused of misbehaviour in a development that mirrors the action after the 2010 World Cup, when four players received bans.
The players' alleged offences are as follows:
Nasri - Launched a foul-mouthed tirade at a journalist after France's quarter-final defeat to Spain.
Ben Arfa - Allegedly involved in a dressing-room bust-up after the 2-0 group stage loss against Sweden.
Menez - Accused of insulting his captain, goalkeeper Hugo Lloris.
M'Vila - Ignored coach Laurent Blanc as he left the pitch when substituted against Spain.
French Federation president Noel Le Graet also announced that the players' bonuses had been frozen.
He said: "I don't like to punish, by nature. I don't like to deliver a hasty opinion. But our players should be punished or sanctioned."
"I don't want them thinking they are victims. They are not."
Le Graet also denied reports in the French press that Didier Deschamps had turned down the chance to replace Blanc as coach.
He said: "I saw this morning that Deschamps had said 'no'. That's a mistake. He's a boy that I would like to work with."
Deschamps has until the end of the week to decide whether to take the job.