The episode on Dec. 17 in Paris had supporters fighting and some of them coming onto the field to throw flares at each other at half-time when the score was level at 1-1.
It was the latest in a series of incidents that has marred French football this season, leading FFF president Noel Le Graet to say it was "disastrous" and "shameful."
The FFF's disciplinary commission also fined Lyon €52,000 ($58,890) while second-tier Paris FC were handed a €10,000 fine.
Lyon fans have been barred from attending away matches in domestic competitions for the rest of the season.
Lyon also received a suspended ban from the French Cup for the 2022-23 season with a warning that they will be thrown out again if their fans are guilty of violence which results in the match being stopped.
As a result of the FFF's decision, Nice directly advanced to the next round.