However the Nato-led International Security Assistance Force (Isaf), in a statement, said: "An Isaf soldier died as a result of a firefight in southern Afghanistan."
It said two other Nato soldiers were injured in the Friday morning battle but did not give any other details about the location of the incident or the nationality of the troops.
There was no way of independently verifying either account.
The US-led forces also said in a statement on Friday that US and Afghan troops backed by warplanes killed more than 35 Taliban fighters during a five-hour battle on Thursday afternoon.
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Also on Thursday, Chirac called Hamid Karzai, his Afghan counterpart, to "demand his support" for efforts to free two French aid workers kidnapped 10 days ago, Karzai's office said.
In a statement on Friday, Karzai's office said: "The president in response assured that all relevant Afghan authorities will do their utmost to secure their release."
The French aid workers, from the non-governmental organisation Terre d'Enfance (A World for Our Children), went missing on April 3 in the south-western province of Nimroz.
The Taliban says it is holding the pair, a man and a woman, along with three of their Afghan colleagues.
On Sunday, the Taliban said that it had beheaded an Afghan reporter whom they kidnapped with an Italian journalist a month ago in the southern province of Helmand.
Ajmal Naqshbandi was killed after Karzai's administration failed to negotiate with the Taliban.
However, Italian reporter Daniele Mastrogiacomo was freed in a hostage deal that saw five Taliban released from Afghan jails.
Karzai was criticised both within and outside Afghanistan for his controversial deal and has said that his government will not repeat the hostage trade with the Taliban.