The messages on Twitter and other sites called for demonstrations to be held Saturday in Paris, Marseille and other major cities, a week after police in the capital arrested 150 people for taking part in a rowdy protest near the US embassy.
Most messages read "Don't touch my Prophet", a variation of the French anti-racism slogan "Don't Touch my Mate" popular in the 1980s.
An individual had also placed a request for permission to demonstrate Saturday outside the biggest mosque in Paris, a source told AFP.
It was not clear who was behind the appeal that comes after France's interior minister said he will prevent any further such demonstrations taking place.
"These protests are forbidden. Any incitement to hatred must be fought with the greatest firmness," Manuel Valls said Sunday.
He said that among the roughly 250 protesters on Saturday there were some groups that "advocate radical Islam", but they were not representative of the moderate Islam practised by most Muslims in France.
France is home to Western Europe's largest Islamic community, with at least four million Muslims in the country.
Protests have been staged since last Tuesday in at least 20 countries, with more than 30 people killed and dozens wounded in violence linked to the film that mocks the Prophet Muhammad and portrays Muslims as gratuitously violent.