After a sixth consecutive loss across all competitions on Sunday - 3-1 at Lorient in Ligue 1 - Nice players were confronted by a large number of their supporters when they returned to the club's training and academy centre.
Players and staff were reportedly assaulted and fans shouted insults and demanded greater commitment from the squad.
Nice prosecutor Damien Martinelli said on Tuesday that two players, whom he did not identify, filed a complaint.
An investigation has been opened for aggravated assault, participation in a group preparing acts of violence or vandalism, and failure to prevent an offence against physical integrity, he said.
Martinelli said the players reported having been punched, kicked, and spat on while being insulted by supporters, many of whom had their faces covered, before managing to flee toward the training centre.
"The club understands the frustration caused by the series of poor results and performances that fall short of its values," Nice said in a statement.
"However, the incidents that occurred during this gathering are unacceptable. Several members of the club were confronted and targeted. OGC Nice offers them its full support and condemns these actions in the strongest possible terms."
According to l'Equipe newspaper, players Jérémie Boga and Terem Moffi took multiple blows, including to the head and groin, while sporting director Florian Maurice was also assaulted. L'Equipe and RMC said that Boga and Moffi have been given medical leave.
The French league said the assaults were "completely unacceptable, undermining the integrity of the participants in the game and the values of football." They added that they will join as a civil party in the complaints filed by the players to ensure that the incidents are thoroughly investigated.
Sports Minister Marina Ferrari joined in the criticism, posting on X that the incidents had "nothing to do with true fan culture."
"I will always defend those who bring life and energy to our stadiums, but never those who resort to violence, who must be held accountable for their actions," she said.
