The attack on the soldiers, who were unarmed, came on Friday at a base in eastern Afghanistan and left 15 other French troops wounded, eight of them seriously.
French President Nicolas Sarkozy reacted angrily, threatening to pull his forces out of Afghanistan ahead of the 2014 deadline for all US-led coalition combat troops, and dispatched Defence Minister Gerard Longuet to Kabul.
That started a round of claim and counter claim over who was responsible for the attack, with Longuet saying he was told the killer was a Taliban infiltrator in the ranks of the Afghan army.
The Taliban, usually quick to claim coalition deaths, said they were still investigating and suggested some of the many attacks by Afghan soldiers on their foreign counterparts were prompted by anger towards the "invading enemy".
Afghan President Hamid Karzai, in a statement after a meeting with Longuet, failed to echo his accusation against the Taliban and also played down the idea of Afghan resentment of foreign troops.
"The attack against French forces by an Afghan army soldier does not represent the anger of Afghan people but it is just an isolated and individual action," he said.
The story emerging from the interrogation of the soldier arrested for the killings -- named as 21-year-old Abdul Mansour -- would support Karzai's interpretation.
"During the initial interrogations by French soldiers, he told them he did it because of the video in which American soldiers were urinating on bodies," an Afghan army officer told AFP.
That report was backed by an intelligence source and another with access to information from the Afghan ministry of defence, both of whom requested anonymity.
The intelligence source said the soldier told interrogators he had no direct contacts with the Taliban.
The Afghan soldier had also referred to a video showing British soldiers allegedly abusing Afghan children, the ministry of defence source said.
Less than a week after news of the US Marines video broke, British military police arrested two servicemen over allegations that they abused an Afghan boy and a girl, both aged about 10, and filmed the incidents.
The US video, posted online this month, showed four US soldiers urinating on three bloodied corpses, and one of the men, apparently aware he was being filmed, saying: "Have a great day, buddy," referring to one of the dead.
The images conjured up previous abuses committed by US troops during the decade-long war against Taliban insurgents and top US officials scrambled to condemn the soldiers.
Told that AFP was about to run reports of the Afghan soldier's alleged confession, a spokesman for the US embassy in Kabul, Gavin Sundwall, said: "Our deepest condolences go out to France and the families of the soldiers who lost their lives in this tragic incident."
The actions in the video "violate the core values of both our societies", he added.
The bodies of the four French soldiers were flown back to Paris late on Sunday, accompanied by French Defence Minister Gerard Longuet.
Sarkozy sent his defence minister to Afghanistan after the attack to evaluate ways to improve the security of the French troops who are training up the Afghan army.
A spokesperson for the British embassy in Kabul said an investigation into the allegations against the British troops was under way and therefore the embassy could not comment on the Afghan soldier's claim.
The US, Britain and France are the main contributors to the coalition forces of some 130,000 troops who have been fighting a 10-year insurgency by hardline Islamist Taliban forces ousted from power after the 9/11 attacks in the US.