In the aftermath of Saturday's fixture at the Allianz Riviera - which the visitors won 1-0 thanks to a second-half goal from Floyd Ayite - Nice fans invaded the pitch in an attempt to reach the Bastia players.
Scuffles broke out before the Bastia players were escorted back to the dressing room by police and stewards.
LFP president Frederic Thiriez released a statement on Sunday, declaring that such incidents will not be tolerated and that disciplinary proceedings will likely be opened.
"The facts that occurred last night at the end of the match between Nice and Bastia are shocking and unacceptable," he said.
"Such images of fights between players and fans, although fortunately no serious injuries were to deplore, are all that we do not want to see in football.
"We must now establish responsibility to take the inevitable punishment to come. I requested a report to the delegates on site for Thursday and the disciplinary committee will review the folder. Provisional measures may be taken.
"Faced with violent behaviour, our line needs more than ever to remain that of zero tolerance. We will not relax our vigilance!"
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