The Taliban abducted Damfreville last month, along with another French aid worker, Celine Cordelier, and three Afghans working for Terre d'Enfance, an agency helping children in southwestern Afghanistan.
Cordelier was released a week ago as a "gesture of goodwill", the Taliban said at the time, because of progress made during three weeks of negotiations since the kidnappings.
Taliban fighters have demanded the withdrawal of French forces from Afghanistan and the release of jailed members by the Afghan government.
Hamid Karzai, Afghanistan's president, said this week that efforts were under way to secure Damfreville's release after calls from Jacques Chirac, France's president, for him to intervene.
The five aid workers were kidnapped in the southeastern province of Nimroz, sandwiched between Iran and Afghanistan's opium centre of Helmand.
Taliban fighters are also holding five Afghan health workers and have threatened to kill one soon unless the government begins peace talks.