In a statement, the French Defense Ministry said the troops also controlled a bridge over the Niger River, The New York Times reported.
Goa is the stronghold of one of the Islamic extremists groups that captured the region.
Earlier reports by witnesses had placed the troops in Hombori, about 155 miles southeast of Goa on Friday.
About 2,500 French troops are on the ground in Mali.
The apparent advancement into Gao came as an al-Qaida-linked group offered to negotiate for the release of a 61-year-old Frenchman kidnapped last year, Radio France Internationale reported.
Gilberto Rodriguez Leal was traveling through western Mali when he was abducted Nov. 20.
Responsibility for his kidnapping was claimed by the Movement for Openness and Jihad in West Africa.
West African military leaders were meeting in Abidjan, Ivory Coast, Saturday to discuss how they could send more troops to Mali as soon as possible.