President Francois Hollande held a top-level security meeting after the overnight attack, which took place as France was on high alert for the Euro 2016 football championships.
Sources close to the investigation identified the suspect, who was killed in a dramatic police operation, as Larossi Abballa, 25.
They told AFP he had been previously sentenced for a role in a jihadist group with links to Pakistan.
He stabbed the policeman repeatedly outside his home in Magnanville, a northwestern suburb of Paris, before holing up inside with the policeman’s partner and the couple’s three-year-old son.
Loud detonations were heard at the scene as elite RAID police moved in following failed negotiations with the attacker.
Officers found the woman’s body after they stormed the house, and her attacker was killed during the assault, interior ministry spokesman Pierre-Henry Brandet said.
The couple’s toddler son was “in shock but unharmed,” a prosecutor added, saying the boy was receiving medical attention.
The slain policeman was 42 years old and worked in nearby Les Mureaux. His partner was a local police official. Their identities have been withheld.
Witnesses told investigators the man may have shouted “Allahu akbar” (God is greatest) as he stabbed the policeman.
Sources close to the inquiry, speaking on condition of anonymity, said he claimed allegiance to IS while talking to officers.
The SITE Intelligence Group, a US-based monitor, cited the IS-linked Amaq News Agency as saying on its Telegram channels: “Islamic State fighter kills deputy chief of the police station in the city of Les Mureaux and his wife with blade weapons near #Paris.”
Abballa, the sources said, had been sentenced in 2013 to a three-year term, six months of which were suspended, for “criminal association with the aim of preparing terrorist acts,” in a trial with seven other defendants.
Hollande met at the Elysee presidential palace early Tuesday with Prime Minister Manuel Valls, Interior Minister Cazeneuve and Justice Minister Jean-Jacques Urvoas.
In a statement earlier, Hollande said an “odious act” had been committed and vowed to shed all light on the murders.
The operation in Magnanville saw police move in quickly to evacuate residents from the neighbourhood and block off roads, an AFP journalist saw.
A helicopter was on the ground a few hundred metres (yards) away from the scene of the attack, along with fire trucks and ambulances.