The picture showed a soldier with his gun in his hand wearing a shoulder insignia bearing the French flag, the number 32 and the motto of Adolf Hitler's SS — "My honour is called loyalty" — said news channel BFMTV. The army took the photo down on Friday.
"This is an unacceptable attitude that doesn't reflect the reality of the armed forces," said army spokesman Colonel Gilles Jaron.
He said the soldier would be "immediately suspended" as soon as he had been identified.
"This soldier was wearing a shoulder insignia that isn't part of the military uniform and which bore an inscription concerning an ideology that is unequivocally condemned," he said.
BFMTV said the army had posted the photo on its Facebook page for its overseas operations.
France has deployed 1,600 soldiers to the Central African Republic, a former French colony, to bolster an African peacekeeping force that was struggling to deal with an outbreak of Christian-Muslim violence following a March coup by a mainly Muslim rebel group.
The French army also faced controversy in January when news media published a picture by an AFP photographer showing a soldier posing in a skeleton mask during his deployment to Mali.
That photograph shows a soldier hiding his face from the desert sand using a scarf resembling a death mask. It is reminiscent of a character in the popular combat video game Call of Duty.