Borghi, from Grenoble in southeastern France, was brought to the Interior Ministry's headquarters in Kabul at about 4:30 p.m. (1200 GMT) and left in the company of French embassy officials less than an hour later, ministry spokesman Sediq Sediqqi said.
He was in good health, Sediqqi said. The French embassy declined to comment.
Borghi was snatched by four armed men from a street in a busy area of the capital Kabul on Nov. 28 and had been held in several locations, including the back of a vehicle, the Afghan official said.
He said it was likely that Borghi was first taken by organized criminals and then sold to insurgents.
The captors, wearing turbans wrapped around their faces, had filmed Borghi several times and told him they were, variously, Taliban, Haqqani and al Qaeda, the official said.