The man who killed a French police officer and his partner claimed allegiance to Islamic State (IS), the BBC is reporting officials as saying.
The AFP news agency says prosecutors have launched an anti-terror investigation after witnesses reported hearing the attacker shouting "Allahu akbar" (God is greatest) during the attack.
The Monday night incident in Paris left a three-year-old boy is without his parents.
The incident unfolded when the policeman was stabbed repeatedly outside his home in the suburb of Magnanville.
The suspect then took the policeman's wife and three-year-old son hostage.
After police stormed the house, authorities told media the hostage situation had been "neutralised".
The suspect was killed and police then found the policeman's wife dead inside the house. The young boy was rescued safely.
Earlier, an Interior Ministry spokesman told The Telegraph the attacker's identity and motives were unknown.
French newspaper Le Parisien said the suspect was a neighbour of the victim.
Islamic State's Amaq news agency claimed an IS fighter carried out the attack.