The Ifop poll found 42 percent believe Mohammed cartoons seen as offensive by many Muslims should not be published. Fifty percent said they backed "limitations on free speech online and on social networks."
However, 57 percent said opposition from Muslims should not prevent the cartoons being published, according to the poll, published in Le Journal du Dimanche.
The poll found overwhelming support — 81 percent — for stripping French nationality from dual nationals who have committed an act of terrorism on French soil.
Sixty eight percent favoured banning French citizens from returning to the country if "they are suspected of having gone to fight in countries or regions controlled by terrorist groups," such as Syria.
The same percentage backed bans on people suspected of wanting to join jihadist movements from leaving France.
However, 57 percent of respondents to the poll opposed French military intervention in countries including Libya, Syria and Yemen.
The poll was conducted last week in the wake of the slaughter at Charlie Hebdo's office in Paris, where Islamist gunmen killed 12 people, saying they were taking revenge for repeated publication by the magazine of Prophet Muhammad caricatures.
On Saturday, five people were killed and churches were set on fire in Niger in the latest protests by Muslims against Charlie Hebdo's decision after the massacre to print another Mohammed cartoon.
French Foreign Minister Laurent Fabius condemned the violence in Niger while President Francois Hollande called freedom of expression "non-negotiable".
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