Nasri was punished for shouting "Shut your mouth" to television cameras following his goal in the 1-1 group-stage draw with England in a tirade he later said was aimed at a journalist who wrote a critical article.
He then directed a string of foul-mouthed insults at an AFP journalist after the quarter-final defeat to Spain in Donetsk.
Jeremy Menez, of Paris Saint-Germain, was given a one-match international ban following a spat with captain Hugo Lloris in the game against Spain and for insulting the referee after the same match.
Nasri, Mvila and Ben Arfa appeared personally before the FFF disciplinary commission, but refused to comment after their hearing.
Lawyer Carlo Alberto Brusa, representing Menez, who is currently on tour in the United States with PSG, described the outcome as "fair" and said he would be advising his client not to appeal.
In addition, Newcastle United's Hatem Ben Arfa and Yann M'Vila, of Rennes, were both issued with warnings.
Ben Arfa — whose father and agent came to blows outside the FFF headquarters on Friday morning — had been called before the disciplinary committee to explain an altercation with then-coach Laurent Blanc in the changing rooms after the 2-0 defeat to Sweden.
M'Vila had been asked to explain his refusal to shake substitute Olivier Giroud and Blanc's hands when he was replaced against Spain.
A statement released by the disciplinary committee of the FFF added that all or part of the players' bonuses would be withheld.
The case came two years after France players went on strike during the World Cup in South Africa that led to the suspension of four players, including Nicolas Anelka for a record 18 games, Patrice Evra for five games and Franck Ribery for three.
The players have ten days to appeal the decision.