"This release is the result of the efforts made for more than three weeks.
They must continue with the same determination and the same discretion until the release of the other hostages."
Qari Yusuf Ahmadi, a Taliban spokesman, said the woman, identified only as Celine, was freed as a gesture of goodwill in the southern province of Kandahar, the Taliban's heartland.
He also said: "We have extended the deadline for the French man and three Afghan hostages for another week."
The four other hostages captured with her are also members of Terre d'Enfance, an agency working with children in Afghanistan's southwest.
Antoine Vuillaume, chairman of the agency, said: "Celine is extremely worn out after 24 days in captivity. She is very weak.
"Clearly this is a first sign of hope. In any case it is a first result, it is a great relief, and brings hope for the other four people."
The Taliban's spokesman said Celine was carrying a message to the French government that it must "cut its military assistance to Afghanistan" and release Taliban prisoners held by the Afghan government.
France pulled 200 French special forces out of Afghanistan late last year, but still has about 1,000 troops stationed in the country.