Samir Nasri, Hatem Ben Arfa, Jeremy Menez and Yann M'Vila will reportedly appear before a French Football Federation (FFF) disciplinary panel just before the end of the month.
The hearing into the players' behaviour during France's Euro 2012 campaign has been set for July 27, according to AFP.
It is believed that Nasri is running the greatest risk of suspension, having caused controversy by launching a foul-mouthed tirade at the press box following his equaliser in Les Bleus' tournament opener against England. He was then involved in a heated exchange with a journalist following the quarter-final defeat to Spain.
Ben Arfa, meanwhile, reportedly had a dressing-room dispute with France boss Laurent Blanc after the 2-0 loss to Sweden, but assistant coach Alain Boghossian subsequently claimed that the pair shook hands soon after.
Menez landed himself in hot water for both insulting the referee in the Spain game, an indiscretion that earned him a yellow card, and then snubbing his captain, Hugo Lloris, though the latter show of disrespect was sorted out among the players concerned.
As for M'Vila, he refused to shake hands with Olivier Giroud, his replacement, or Blanc after being replaced against La Roja, but he later apologised for his actions.