Nice have been docked two points, one of which is suspended, and their French Ligue 1 match with Marseille will be replayed in a neutral location without fans after it was abandoned amid crowd trouble last month, the LFP said on Wednesday.
Nice supporters threw water bottles as Marseille were about to take a corner and, after visiting forward Dimitri Payet hurled one back at them, a full-scale brawl ensued and some fans rushed on to the field.
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Marseille defender Alvaro Gonzalez was banned for two games for his role in the fracas, while Payet was handed a suspended one-game ban. The club's physio Pablo Fernandez was given a nine-month touchline suspension.
Both clubs had been summoned to a disciplinary hearing after the match at Nice's Allianz Riviera was abandoned in the 75th minute.
The LFP had already ordered Nice to play their next home game behind closed doors, pending the results of the probe.
Players from the Nice and Marseille teams retreated to the tunnel and play was held up for 90 minutes before referee Benoit Bastien declared the match abandoned.
Marseille were fifth in the standings with seven points from three matches, a place behind Nice on goal difference before the verdict.