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The federation added that Didier Deschamps, who has just left his job at Olympique Marseille, had asked for time to think about taking over from Laurent Blanc as France coach.
Deschamps has until the end of the week to make his decision, said FFF president Noel Le Graet.
"Hatem Ben Arfa, Yann Mvila, Samir Nasri and Jeremy Menez are summoned to appear before the disciplinary committee," Le Graet told a news conference.
Nasri insulted a reporter after the 2-0 quarterfinal 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 also said the bonus money of 100 000 euros ($125 800) due to Nasri, Menez, Mvila and Ben Arfa for reaching the last eight in Poland and Ukraine had been "frozen".
