Rioters rammed a car into the home of a mayor in southern Paris before setting it on fire while his wife and children were sleeping.
Protesters chased Melanie Nowak and her two children behind the house and into the garden as the family tried to escape.
The mother suffered a serious leg fracture after trying to push her children over the wall that separates her garden from her neighbour’s backyard and was recovering in hospital on Sunday morning. One of the children was also injured.
The country has been rocked by riots after the police killing of Nahel Merbouz, 17, a French teenager of North African descent last week, who was shot at point blank range during a traffic stop.
Gérald Darmanin, the interior minister, on Sunday praised authorities for their “resolute action” which had led to a “calmer night”.
On Saturday evening, police made 719 arrests throughout France, compared to 1,311 arrests made the night before.
Mr Darmanin promised justice for Mr Jeanbrun and his family, “victims of a cowardly and terrible attack”.
“An investigation for attempted murder has been opened and significant resources of the judicial police are mobilised. The perpetrators of these facts will answer for their heinous acts,” he tweeted
Vincent Jeanbrun, the mayor of L’Haÿ-les-Roses, a suburb south of Paris, said the attack on his family was an “assassination attempt”.
“Last night, a milestone was reached in horror and ignominy,” said Mr Jeanbrun, who is also the spokesman for the conservative Republican party.