Nice have managed just one win in their last seven Ligue 1 games.
Reports have suggested that Roy will remain at Nice as their general manager.
Roy’s assistant, Rene Marsiglia, will take control of first-team affairs.
Club president Jean-Pierre Riviere told newspaper Nice Matin: “Eric has not failed. We need a sporting manager, someone who knows the club well.
“Rene Marsiglia knows the game and the players. He is up to this challenge.”