The victims were discovered by their father when he returned home from work, Sky News reported.
Police said they were "actively looking" for the mother, who is in her 40s.
Investigators said the two younger children were dead but the oldest boy was still alive when officers arrived. He later died of his injuries.
"The children had their throats slit but we are still awaiting forensic reports," a police official said.
The family's home is in Dampmart, about 19 miles east of Paris, in the Seine-et-Marne region.