The French Embassy in Kabul said today that the woman, named as Celine Cordelier, flew home overnight. However, a second French aid worker, a man, and three Afghans who were abducted with Cordelier on April 3 remain in captivity. The Taliban say they want French troops in Afghanistan to leave.
Taliban spokesman Zabiullah Mojahed told RFE/RL that the Taliban would give the French government one more week to negotiate the release of a French male aid worker and three Afghans still being held hostage.
"Because we are merciful towards women, and we ended our investigation about her, she was not involved," Mojahed said. "So today at 11 o'clock we released her. We have given her a letter to carry to the French government. And we have issued a seven-day ultimatum because of the French election [on May 6]. We will decide what to do after the election. We want to see the stance of the French government."
The hostages worked for a small French aid group in Afghanistan and went missing in the southwestern province of Nimroz on April 3.
The Taliban had threatened to kill all of the hostages if the French government failed to withdraw all of its troops from Afghanistan by April 27.
The kidnappers also have demanded that Afghan authorities release some Taliban fighters who have been captured in recent months.
Italy and Afghanistan came under strong criticism recently after they agreed to trade Taliban prisoners in order to secure the release of an abducted Italian journalist.
(with material from agency reports)