The French military, however, said that the incidents never happened and the report was "erroneous information."
The documentary, due to air next year and seen by Reuters on Tuesday, says the troops could have killed the al-Qaeda leader in Afghanistan but the order to shoot never came, possibly because it took too long to request it.
"In 2003 and 2004 we had bin Laden in our sights. The sniper said 'I have bin Laden'," an anonymous French soldier is quoted as saying.
The documentary 'Bin Laden, the failings of a manhunt' is by journalists Emmanuel Razavi and Eric de Lavarene, who have worked for several major French media outlets in Afghanistan. A cable television channel plans to air the documentary in March.
Razavi said the soldier told them it took roughly two hours for the request to reach the US officers who could authorize it but the anonymous man is also quoted in the documentary as saying: "There was a hesitation in command."
French army: That never happened
Razavi told Reuters several sources told them the sightings were six months apart and they declined to be more specific.
French armed forces spokesman Christophe Prazuck said "that never happened" when asked about the bin Laden sightings.
Bin Laden, the mastermind behind the September 11 attacks on the World Trade Center and the Pentagon, is believed to be hiding in the mountains along the Afghanistan-Pakistan border.
France has roughly 200 elite troops operating under US command near Afghanistan's border with Pakistan. Paris announced on Sunday it was withdrawing them at the start of 2007.
France is part of the 32,000-strong NATO-led International Security Assistance Force in Afghanistan, which took over command of a war against the Taliban from US-led forces in October and has launched a series of military offensives.
Its special forces were deployed in 2003 to bolster Operation Enduring Freedom, a US-led campaign against the Taliban and al-Qaeda in response to the September 11 attacks.
Afghans questioned in the documentary said they believed the United States was not interested in finding bin Laden, despite the USD 25 million price Washington has placed on his head.
The documentary stopped short of that conclusion but raised questions about the US hunt for bin Laden, such as whether Washington is more concerned about preserving stability in Pakistan, where many support bin Laden, than in finding him.
In September, President Bush dismissed as an "urban myth" the idea his administration had become distracted from its effort to track down bin Laden.