Authorities said the incident was an apparent attempt to burn down the local official's house.
An investigation has been opened into the attempted murder of the mayor of L'Haÿ-les-Roses (Val-de-Marne) following a car-ramming attack on his home on Saturday night, the Créteil public prosecutor's office said
Mayor Vincent Jeanbrun's wife and one of his two young children were injured in the attack, according to the mayor, who condemned "an unspeakably cowardly assassination attempt".
The judicial police are handling the investigation, according to the public prosecutor's office.
According to Créteil public prosecutor Stéphane Hardouin, the attackers probably intended "to burn down the house".
"Initial findings lead us to believe that the vehicle was launched to burn down the bungalow", the public prosecutor told the press. "An accelerant was discovered in a bottle of coke", added the magistrate, denouncing the events as "extremely serious".
Prime Minister Elisabeth Borne travelled to the town on Sunday to lend her support the mayor. In a public appearance, she assured all French mayors that the government would not "allow any violence to go unchallenged" and that "the utmost firmness" would be applied in imposing penalties.
"We were all very shocked" by this "intolerable" attack, Ms Borne told the press after an hour-and-a-half visit to the town hall and the municipal police.
She also acknowledged that the problem of threats to public figures ran far deeper than a single attack.
At the meeting at the town hall, Borne said the government had been working for several months on issues of violence against elected representatives, and that is also "looking at how we can support towns that have had facilities destroyed".
"We're not going to leave you alone, we're going to stand by the mayors, including mayors who have problems supporting young people during the holidays", she said.
Other French politicians have been unanimous in their condemnation.
"To attack the life of an elected representative and that of his family is to attack the nation", wrote Senate President Gérard Larcher on Twitter. "Public commitment should never be synonymous with danger, either for oneself or for those one loves", said National Assembly President Yaël Braun-Pivet.
L'Haÿ-les-Roses sits a few kilometres to the south of Paris, towards Orly airport.
France has seen several nights of widespread urban violence sparked by the police shooting of an unarmed teenager in Nanterre. On Saturday night alone, more than 700 people were arrested and 45,000 police officers deployed to control the situation.