The French military targeted Syria's main chemicals research centre and two chemical production facilities overnight, officials said, adding that the air strikes were over but the military was ready to act upon request.
President Emmanuel Macron ordered the military intervention in Syria alongside the United States and Britain in response to a poison gas attack that killed dozens of people last week.
"This action was proportionate and targeted, it was not aimed at (Syrian President Bashar al) Assad's allies nor at the civilian population," Foreign Minister Jean-Yves Le Drian said in a televised statement.
"It was limited to specific objectives: the destruction of the Syrian regime's chemical capabilities to stop it from committing new chemical massacres."
Defence Minister Florence Parly said cruise missiles had been fired, in coordination with the United States and Britain. The operation was carried out at 3am (0100 GMT), she said, adding naval and air means had been used, including an air raid launched from several air bases in France.
"We are not looking for confrontation and refuse any logic of escalation, that is the reason why we, with our allies, ensured the Russians were warned beforehand," Parly said.
While there had been general public warnings broadcast by US President Donald Trump, Macron himself and other Western leaders, a French presidency source clarified that the French leader did not tell Russian President Vladimir Putin the allies would strike overnight when they talked over the phone on Friday.
Regular "deconfliction" contacts were made with the Russian military once the operation had been kicked off to make sure that they would not be accidentally hit, the source said.
The French presidency issued a video on Twitter showing what it said were war planes taking off as part of the intervention.
"On April 7, dozens of men, women and children were massacred in Douma, with the use of a chemical weapon in a total violation of international rules (...) The red line established by France in May 2017 was crossed," Macron said in a statement.
He said the attack had been limited so far to Syria's chemical weapons facilities and said the facts and the responsibility of the Syrian regime were beyond doubt.
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