The country's Interior Ministry announced it will crack down on any kind of protest against the cartoon that denigrated the Muslim prophet.
Interior Minister Manuel Valls said prefects throughout the country had orders to prohibit any protest over the issue and to crack down if the ban was challenged.
"There will be strictly no exceptions. Demonstrations will be banned and broken up," he told a news conference in the southern port city of Marseille.
The main body representing Muslims in France appealed for calm as the satirical weekly Charlie Hebdo put a new print run of the cartoons featuring a naked Muhammad on the news stands.
The drawings have stoked a furor over an anti-Islam film made in California that has provoked sometimes violent protests in several Muslim countries, including attacks on U.S. and other Western embassies, the killing of the U.S. envoy to Libya and a suicide bombing in Afghanistan.
French embassies, schools and cultural centers in some 20 Muslim countries were closed on Friday, the Muslim day of prayer, in a precaution ordered by the French government.
Police were on alert in the French capital after protests planned by some Muslim groups were banned.