Calls to protest against the film, which has had insulting references to the Prophet Mohammed dubbed into it, have been issued on Facebook, Twitter and other social networks this week after police broke up an unauthorised demonstration in Paris last Saturday.
Despite appeals for calm by French Muslim leaders, demonstrations are expected to take place in several cities next Saturday, although Ayrault only mentioned banning the Paris one.
There is “no reason why we should let conflicts which do not concern France come to our country”, Ayrault told RTL radio on Wednesday. “We are in a republic which has no intention of allowing itself to be intimidated by anyone at all over its values.”
He also said that people offended by Wednesday's publication of cartoons of Mohammed by Charlie Hebdo were free to sue the satirical paper but that the state would not intervene.
Interior Minister Manuel Valls on Monday claimed that “small groups that we know are active in our neigbourhoods, advocating radical Islamism” were present at last Saturday’s protest along with women with their faces covered, in breach of French law.
“I will not tolerate that completely veiled women, prayers in the street, that slogans against allied countries and our values can be heard on our streets,” he told France 2 television.
Police arrested 150 of the roughly 250 people present at last weekend’s protest.
France’s opposition UMP has slammed Paris police for failing to prevent it and the right-wing Le Figaro on Wednesday predicted that “if we don’t watch out they will be 1,000 tomorrow and many more the day after”.
More than 30 people have died during the worldwide demonstrations and bombings that have followed to the posting of a trailer for Innocence of Muslims posted on the internet.
About 1,000 protesters, mostly students, blocked the Jalalabad-Kabul road in Afghanistan on Wednesday, the day after a female suicide bomber killed 12 people in Kabul.