Foreign Minister Laurent Fabius warned that Charlie Hebdo could be throwing "oil on the fire," but said it's up to courts to decide whether the magazine went too far.
The magazine's crude cartoons played off the film and ridiculed the violent reaction to it. Riot police took up positions outside the offices of the magazine, which was firebombed last year after it released an edition that mocked radical Islam.
Charlie Hebdo's chief editor, who goes by the name of Charb and has been under police protection for a year, defended the cartoons.
"Muhammad isn't sacred to me," he said in an interview at the weekly's offices, on the northeast edge of Paris amid a cluster of housing projects. "I don't blame Muslims for not laughing at our drawings. I live under French law; I don't live under Quranic law."
Government authorities and Muslim leaders urged calm.
"This is a disgraceful and hateful, useless and stupid provocation," Dalil Boubakeur, rector of the Grand Paris Mosque, told The Associated Press. "We are not Pavlov's animals to react at each insult."
A small-circulation weekly, Charlie Hebdo often draws attention for ridiculing sensitivity around the Prophet Muhammad, and an investigation into the firebombing of its offices last year is still open. The magazine posted a statement online saying its website had been hacked.
Abdallah Zekri, president of the Paris-based Anti-Islamophobia Observatory, said his group is considering filing a lawsuit against the magazine.
"People want to create trouble in France," he said. "Charlie Hebdo wants to make money on the backs of Muslims."
Charlie Hebdo was acquitted in 2008 by a Paris appeals court of "publicly abusing a group of people because of their religion" following a complaint by Muslim associations.
Prime Minister Jean-Marc Ayrault said organizers of a demonstration planned for Saturday against "Innocence of Muslims" won't receive police authorization. Paris prosecutors have opened an investigation into an unauthorized protest last Saturday around the U.S. Embassy that drew about 150 people and led to scores of arrests.