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.

Steven Frater, 32, hid 167 diazepam tablets and quantities of heroin and oxymetholene inside his body.
He then stole a television from the Asda store in Galashiels, hoping to be arrested and sent to Edinburgh Prison.
Frater, formerly of Jedburgh, admitted at Selkirk Sheriff Court the theft and refusing an internal examination at Edinburgh Royal Infirmary in February.
The court heard he attempted to defeat the ends of justice by refusing to be examined in hospital knowing he had the controlled drugs inside his body.
However, he was subsequently found to have swallowed a number of substances that he had hoped to distribute in jail.
Sheriff Jamie Gilmour sentenced him to three years in prison for the offences.

In the latest attack on their home, a number of rocks were thrown through the windows.
The woman has said she "can't stop her tears from pouring" and is worried about her children's safety.
The police have appealed for anyone with information to come forward.
The woman, who we are calling Amina, is due to give birth next month. She said she has been unable to sleep or eat since the attack and is worried about the impact that it might have on her unborn baby.
Amina, her husband and children, moved into a hostel following the attack.
"We were out and when we came back, we found the police waiting for us and they told us that someone had broken the windows of the house," she said.
"There was glass everywhere. downstairs and upstairs.
"I just sat on the couch, I couldn't say anything."
In April, the couple had the windows of their car broken and have also previously had eggs thrown at their house and rubbish thrown into their yard.
"I had nightmares  thinking that someone was after us and they wanted to hurt my family," she said.
"It's my responsibility to look after my kids and to keep them in a safe place, it's my responsibility to protect them."
Amina and her family are refugees and have been living in Northern Ireland for about two years.
She said the incident had had a huge impact on her children.
While Amina's daughter is too young to understand what has happened, she said her son had been upset by seeing the glass and seeing his mother crying.
"I tried to explain to my son as simply as I can. I told him there are some bad people in the world and they do bad things," she said.
"I want him to understand what is going on, it's important for him to know."
Amina said she had to try and explain to her son what a race hate crime was.
"I'm sure this will not be the last time he's going to experience this," she said.
"We have to be honest and rational. We are not from here and there are people who don't like foreign people living around them.
"I want him to understand this as soon as possible, so he can be ready for what might happen in the future."
The police have appealed for information.
An Air France aeroplane narrowly missed central Africa's highest mountain in early May, French investigators say.
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A man who swallowed a large quantity of drugs in order to smuggle them into prison has been jailed for three years.
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A pregnant Sudanese woman and her two young children, aged seven and one, have had to leave their home in east Belfast following a racially-motivated hate crime.