David Thomson, a terrorism expert at Radio France Internationale, said the video was posted using the Facebook Live application at 8:52 pm on yesterday.
It has since been removed.
In 13 minutes of footage shot at the home of his victims, Larossi Abballa announced that he had killed a policeman and his wife, said Thomson, author of a book on young French radicals.
"I don't know what to do with him," Abballa says in the footage, indicating the couple's three-year-old child sitting behind him on a couch.
During the assault, he attacked the 42-year-old police officer, stabbing him repeatedly outside his home, before going inside and slitting the throat of his 36-year-old partner, who also worked at a police station.
At the start of the recording, the 25-year-old convicted radical swears allegiance to Islamic State leader Abu Bakr al-Baghdadi.
He then calls on other Muslims to attack "police, journalists, public figures, prison guards and rappers," listing around a dozen well-known figures by name.
Abballa asked his 160 Facebook followers, particularly his IS contacts, "to issue a statement claiming the attack".
The IS-linked Amaq news agency later announced that an "Islamic State fighter" had killed a policeman and his wife near Paris with a knife.
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