Earlier Douste-Blazy had said: "I can confirm that he's freed."
Yousuf Ahmadi, the Taliban spokesman, said: "We released the French citizen today at [1300 GMT] in Maiwand district of Kandahar province. We handed him over to the tribal elders and he was later handed over to the Red Cross Society."
Damfreville was handed to tribal elders in the southern province of Kandahar and then to the International Committee of the Red Cross (ICRC).
Franz Rauchenstein, ICRC deputy head of delegation, also confirmed the release. "He has been handed over to us, it's true, I can confirm," he said.
Damfreville and three Afghan co-workers were captured in southwestern Afghanistan on April 3.
A French woman who was abducted with them, Celine Cordelier, was released on April 28 and made an impassioned plea for the freedom of her colleagues.
Ahmadi said the leading council of the Taliban, which calls itself the Islamic Emirate, decided to free the aid worker because French president-elect Nicolas Sarkozy had suggested France might pull its troops out from Afghanistan.
He said Sarkozy had "said in his speeches that he will think about the withdrawal of French troops from Afghanistan."
Ahmadi said: "The Islamic Emirate hopes that the French president implements into action the promise he has made. About the fate of the three Afghans, the leading council of the Islamic Emirate will decide later."
James Bays, Al Jazeera's correspondent in Kandahar, said: "Sources say the hostage will be handed over to the French military who will fly him to Kabul."