The federation added that Didier Deschamps, who has just left Olympique Marseille and is the favourite to replace Laurent Blanc as France coach, needed time to work out whether he wanted the job.
"Hatem Ben Arfa, Yann M'Vila, Samir Nasri and Jeremy Menez are summoned to appear before the disciplinary committee," FFF President Noel Le Graet told a news conference.
Nasri insulted a reporter after the 2-0 quarter-final defeat by eventual champions Spain while Menez did the same to captain Hugo Lloris.
Ben Arfa was involved in a dressing-room argument with Blanc and Mvila did not shake the coach's hand when he was replaced by Olivier Giroud against Spain.
Blanc declined to renew his contract following the team's defeat.
Le Graet said he had contacted Deschamps to see if the former World Cup and European Championship-winning midfielder was interested in the France job.
"I read this morning that Deschamps had said 'no'. That's a mistake. He's a boy I would like to work with," Le Graet said.
"He said he was not in the right state of mind to think about it right now and asked for a delay."
Asked about when Deschamps needed to confirm his interest, Le Graet said: "By the end of the week would be good".
The new coach will be named "at the end of the week or the beginning of next week," the president added.
Le Graet also said the individual bonus money of 100,000 euros due to the entire squad for reaching the last eight in Poland and Ukraine had been "frozen".
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.