Police in Paris have arrested 21 people who tried to defy a ban on demonstrations against the anti-Islam film that has been causing violent protests in Muslim countries.
The plan had been to march through northern Paris.
French Muslims are also angry at the cartoon depiction of the Prophet Muhammad in satirical magazine Charlie Hebdo.
Those trying to organise demonstrations used the internet to encourage the estimated five million Muslims living in France to take to the streets.
“There were lots of messages and appeals on social networking sites. They were trying to get people to go out and break the law by going out to protest, so we were worried. We tried to calm down the situation,” said one man outside a Paris mosque.
Muslim leaders in France are also encouraging people to follow the law.
A few female protesters and a man who was with them were prevented from unveiling a banner by police in the northern city of Lille.
Elsewhere in France, security was heightened, but protests did not take place.