The Ifop poll found 42 per cent believe such cartoons seen as offensive by many Muslims should not be published. Fifty per cent said they backed "limitations on free speech online and on social networks."
However, 57 per cent 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 per cent -- for stripping French nationality from dual nationals who have committed an act of terrorism on French soil.
The same percentage backed bans on people suspected of wanting to join jihadist movements from leaving France.
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However, 57 per cent 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 attack 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 the cartoons.
French Foreign Minister Laurent Fabius condemned the violence in Niger while President Francois Hollande called freedom of expression "non-negotiable".