A man with a past terrorist conviction shot video footage during a fatal knife attack on two police officers outside Paris, according to French officials.
One official said the assailant posted the video on Facebook Live, the social media site's live feed. His account has been suspended.
At one point during the attack, the assailant puzzled over what to do with the couple's three-year-old child, who survived.
An agency affiliated to Islamic State (IS) cited an unnamed source as saying one of their fighters carried out the attack, but the extremist jihadist group has not officially claimed responsibility.
In the incident in the Paris suburb of Magnanville, a police officer was fatally stabbed outside his house.
His female partner, also a police officer, was found dead after the knifeman was killed in a police raid on the property.
The suspect has been named as Larossi Abbala, a 25-year-old who had a past terrorism conviction for recruiting fighters for jihad in Pakistan.
Abbala was from the western Paris suburb of Mantes-la-Jolie, and was sentenced in 2013 to three years in prison, including six months suspended, for association with a terrorist enterprise.
French president Francois Hollande said the attack was "incontestably a terrorist act".
Speaking at the Organisation for Economic Co-operation and Development (OECD) in Paris, Mr Hollande said France is facing a terror threat on "a very large scale".
He said: "France is not the only country concerned (by the terrorist threat), as we have seen, again, in the United States, in Orlando."
France has been on particularly high alert as it hosts football's European Championship, and is still under a state of emergency after the November attacks.
Prime minister Manuel Valls said: "It's a global threat, that is why we are fighting terrorism in Syria and Iraq, and on our soil."
A Facebook profile bearing the name Larossi Abballa - which vanished from the internet early on Tuesday - showed a photo of smiling, bearded man.
Two recent posts featured videos critical of Israel and Saudi Arabia.
The last post publicly available was a mock-up of the European Championship logo, highlighting the poster's purported masonic and occult symbols.
"Some will say we see evil everywhere," Abballa said in a message posted about 18 hours before the attack.
French interior minister Bernard Cazeneuve said more than 100 people seen as potential threats have been arrested in France this year, including in recent weeks.
Mr Cazeneuve also visited the police station where one of the victims, 42-year-old Jean-Baptiste Salvaing, worked.
After a three-hour stand-off, elite police commandos stormed Mr Salvaing's house, 35 miles west of Paris, after he was stabbed outside it.
France, like other countries in Europe, has seen a series of stabbings aimed at police officers or soldiers carried out by Muslim radicals.
IS has encouraged its supporters to stage such attacks.
In Paris, the Eiffel Tower was lit up in the colours of a rainbow on Monday night to honour victims of Saturday's mass shooting at a gay nightclub in Orlando, Florida, which killed at least 49 people.
The gunman declared his allegiance to IS in phone calls to police, but his motives remain unclear.
Two people have been detained as part of the investigation into the killings. The two were said to be close to the suspected attacker.
No other information has been released about those detained.
Mr Cazeneuve said the investigation is advancing as quickly as possible "to put eventual accomplices out of action".