"Our compatriot Claudia Priest, who was kidnapped at the start of the week in the Central African Republic, is finally free. It's an immense relief for all those who have worked towards this happy outcome," Fabius said in a statement.
Priest, 67, was kidnapped along with a local man in the capital Bangui on Monday. A UN employee was also briefly detained by the anti-balaka the following day.
The abductions were thought to be in response to the arrest of one of the anti-balaka's leaders by UN peacekeepers last Saturday.
The anti-balaka militias protested his arrest on Sunday and Monday in their Boy-Rabe stronghold in the northeast of the city, and several witnesses reported kidnapping attempts and robberies in the neighbourhood.
Violence between rival factions has plunged the deeply impoverished country into an unprecedented political and security crisis. The conflict, which began in 2013, has claimed thousands of lives.
The anti-balaka are mainly Christian militias formed to fight off relentless attacks from mostly Muslim rebels of the Seleka coalition. The Seleka seized power in March 2013 but were routed from Bangui in January last year.