Flight AF953 was travelling from Malabo, the capital of Equatorial Guinea, to Douala, Cameroon's largest city and commercial capital, when it hit bad weather on 2 May.
While avoiding storm clouds, the plane came close to hitting the 4,040-metre (13,254 feet) Mount Cameroon.
French accident investigators BEA have now opened an investigation.
The Boeing 777 aircraft had 37 people on board as it made the short journey to Douala, which is around 100km (62 miles) from Malabo.
It was due to arrive in Cameroon to pick up more passengers before continuing to Paris.
After diverting north to avoid storm clouds shortly after 21:00 local time, the plane's new route to Douala took it directly towards the mountain.
An initial incident report published by BEA said an automated warning, saying "Pull up", was activated. The plane then ascended quickly from 9,000ft (2,743m) to 13,000ft (3,962m) to avoid a collision.
BEA did not say how close the plane came to Mount Cameroon.
The flight landed 44 minutes after leaving Malabo, and no-one was injured.
Air France said they were conducting an internal investigation into the incident.
An Air France aeroplane narrowly missed central Africa's highest mountain in early May, French investigators say.