"There is a certain agitation (in French mosques) about this affair. I hope there will not be any protests in France," said Abdallah Zekri, the head of an Islamophobia Observatory set up by the country's Muslim Council.
The rector of the Paris Grand Mosque, Dalil Boubakeur, called on Muslims not to rise to "this provocaton knowingly perpetrated against Islam", while the Muslim Council said only "legal and fair means" should be used to defend the religion.
The council condemned an attack sparked by the film on the US consulate in the Libyan city of Benghazi, where four Americans including the ambassador were killed.
The movie, titled "Innocence of Muslims", pokes fun at the Prophet Mohammed and portrays Muslims as immoral and gratuitously violent.
France is home to at least four million Muslims and leaders of the community say incidents of Islamophobia are on the rise against a background of confrontation with the authorities.
Many Muslims have been angered by legislation banning women from wearing full veils and this year's elections were marked by debate over the use of halal methods of animal slaughter.