The official, who has close ties to intelligence services but was not authorised to speak publicly about the inquiry, also said another French fighter whose death was announced this week by Islamic State is a young teenager.
The man in the video, released late yesterday, speaks with a southern French accent and looks like the step-brother of Mohammed Merah, who killed seven people in attacks on a Jewish school and paratroopers in the south of France beginning on March 11, 2012 - exactly three years ago.
In addition to the 2012 killings in Toulouse, Jews in a kosher supermarket were among the targets of three days of terror in the Paris area this year that left 20 people dead, including the three gunmen.
"Here are the young lions of the caliphate," the man says in the video. Soon afterward, the child is shown shooting the man in the head.
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French government spokesman Stephane Le Foll described the video as a "dreadful" killing, but refused to comment Wednesday on the nationalities or identities of the man and boy.
According to Europe 1 radio, the child's entire family left last year from the city of Strasbourg to recover the remains of an older brother in Syria, and a second older brother was also killed in the war zone.
About 1,400 people, including entire families, have left France to join extremists in Syria and Iraq, and many have returned.
About 3,000 Europeans are part of the fight, Valls said, adding: "There could be 5,000 before the summer and without a doubt 10,000 by the end of the year.