EU nations should consider action against Turkey, including the threat of sanctions, France’s Europe Minister said.
Clement Beaune told the French Parliament that action could include sanctions against Turkish President Recep Tayyip Erdogan after “provocations”.
"We need to go further," Mr Beaune said. "We will push for strong European responses, which could include sanctions.
The call came as Charlie Hebdo magazine published a front-page cover with a cartoon of Mr Erdogan, which will increase tension.
Ankara summoned the French charge d'affaires on Wednesday because of the caricature, the Turkish Foreign Ministry said.
Turkey has been a vocal critic of France and its President, Emmanuel Macron, for praising teacher Samuel Paty who was murdered for showing cartoons of the Prophet Mohammed.
Paty was killed by a teenage extremist after showing his pupils the cartoons, which are considered blasphemous under Islam, in a lesson on freedom of speech.
UK Foreign Secretary Dominic Raab said that Nato allies should support France against Turkey, which is also a Nato member.
Ankara has also been criticised by France and the EU over natural gas exploration in a contested zone in the Eastern Mediterranean, where Turkey, Greece and Cyprus have a dispute.
Mr Erdogan vented his anger at the "scoundrels" of Charlie Hebdo and his office vowed "legal and diplomatic actions" over the cartoon.
The magazine came out days after he called for a boycott of French products.
Al Qaeda-linked extremists have seized on the growing campaign to incite violence against the country’s political leadership.
France has banned a pro-Hamas group active in the country after it was accused of being directly implicated.