Five dead bodies were found on Christmas Day in an apartment in the town of Meaux to the east of Paris, the local prosecutor told AFP, adding that a homicide inquiry had been opened.
According to news website Actu17, which first reported the discovery, the victims were a woman and her four young children.
It added that police were looking for the 33-year-old father, who was "on the run".
Prosecutor Jean-Baptiste Bladier confirmed that five bodies had been found to AFP.
The Versailles judicial police service is investigating.
The Paris region has recently seen a series of infanticides.
In late November, a 41-year-old man confessed to killing his three daughters, aged four to 11, and turned himself in.
Police found them dead in his home in the town of Alfortville, in the southeastern suburbs of the capital.
A month earlier, in October, a gendarme killed his three daughters before killing himself at his home in Vemars in Val-d'Oise.