The schools inspector in the Haute-Garonne district in southern France said that students in Toulouse believe they recognised the boy, who appears to be no more than 12.
"Concerning the formal identification of this person, I cannot tell you anything," Jacques Caillaut said, adding that "children from the Vauquelin College have recognised one of their classmates, but we must remain cautious."
He said that following the viewing of the video by the shocked students on Wednesday, counselling was put in place for them.
On Thursday, French officials had launched a formal investigation into the video, which also features a French-speaking man.
According to sources close to the investigation, the man is probably Sabri Essid, who has close links to French jihadist gunman Mohamed Merah, the killer of three soldiers, three students and a teacher in southern France in 2012.
In the video, a youth, dressed in an orange jumpsuit and identifying himself as 19-year-old Mohammed Said Ismail Musallam, is shown kneeling in front of the boy. A man stands at his side.
The man seen kneeling recounts how he was recruited by Israeli intelligence, a claim denied by his father.
The man standing nearby, speaking in French, issues threats against Jews in France, before the boy walks around in front of the hostage and shoots him in the forehead using a pistol.
The boy, who shouts "Allahu Akbar" ("God is greatest" in Arabic), then shoots the man four more times as he lies on the ground.
Sources familiar with the case have said the boy may be 31-year-old Essid's stepson.