The show "Merci pour l'Info" (Thanks for the News) obtained the footage, seen by an AFP correspondent, from what the network described as a "European working as a subcontractor for the US army" who left Iraq two weeks ago.
US television network ABC aired the same images on January 9, and the footage has been available on the Internet for several weeks.
The European claims to have hidden the tape - dated December 1, 2003, and filmed at an unidentified location in Iraq - at the US base where he lived and worked.
A French lawyer and member of the International
Federation for Human Rights (FIDH), Patrick Baudouin, told AFP that knowingly killing an enemy who is wounded constitutes a war crime under international law.
The three-and-a-half minutes of footage, to be broadcast at 6:40 pm (1640 GMT), was taken from the helicopter firing at the three individuals, who were considered by the US military to be suspicious.
Conversations between the helicopter pilot, the sharpshooter and their commanding officer - who had a video link and was giving orders in real time - can be heard on the tape.
The footage shows how the three men are killed one after the other. It begins with a sports utility vehicle driven by a man, who joins another man waiting near a truck.
One of the two grabs a long object, which the US soldiers identify as a weapon, and discards it several meters (yards) away. The two, believed to have weapons, are then joined by a third man aboard a tractor.
"Got auto range on him," the sharpshooter says of the first man, whose arms are down by his side.
"Roger. Hit him," orders the officer in charge.
The second man, who attempts to hide behind the tractor after the shooting of the first suspect, is subsequently shot dead.
After the deaths of his two companions, the third man tries to hide under the truck, but is hit by helicopter gunfire.
"Got the guy right here," says the sharpshooter, as the wounded man is seen crawling on the ground.
"Good. Fire. Hit him," replies the officer.
"Wait, some movement by the truck," says the shooter. "He's wounded."
"Hit him. Hit the truck and him. Go forward," answers the officer.
In March, the rights watchdog group Amnesty International said "scores of civilians have been killed apparently as a result of excessive use of force by US troops, or have been shot dead in disputed circumstances."
The broadcast also comes as the United States confronts mounting anger over the alleged abuse of coalition prisoners in Iraq and the release of photos showing US troops humiliating Iraqi detainees.