© AFP
Critics accused the agency, which depends largely on the French state for its financial equilibrium, of self-censorship in an attempt to avoid ruffling Mr Hollande's feathers.
But the row merely added to the publicity surrounding the picture, which went viral on French internet sites amid widespread hilarity.
The photograph, taken when Mr Hollande visited a school in Denain, northern France, to mark the start of the new term on Tuesday, made him look like a clown with an expression of stupefaction in his eyes, according to Le Point, the news magazine.
Rue 89, a news site, said he looked "simple-minded".
The picture, taken by Denis Charlet, one of AFP's photographers, was made available to the media outlets which subscribe to the agency.
It was among a series of photographs showing Mr Hollande at a teacher's desk, most of which had him looking earnest if not statesmanlike.
Hours later, however, AFP sent out a message to say the unflattering photograph had been withdrawn because of "an editorial issue".
A red cross was placed over the picture which was accompanied by the words: "Mandatory Kill".
Jean-Marc Morandini, a respected media affairs commentator, denounced an act of censorship on his blog, whilst other analysts claimed that the photograph had been withdrawn on the orders of the French presidency.
Philippe Massonnet, the global news director at the agency, said: "AFP was subjected to no pressure from the summit of the state. This was an editorial decision taken in our Paris news room in all independence after an internal debate.
"The authorities would never ask us that sort of thing. It was decided to kill the picture because we judged afterwards that it brought nothing to the series in terms of news."
But Renaud Revel, a media commentator with L'Express magazine, said AFP's move had backfired, at least in terms of the Head of State's image.
By the time the picture had been officially removed, it was already circulating on the internet and the decision to censor it merely added to its popularity, he said.
"AFP has unleashed a storm of mockery on the web, where this photograph is a hit,' said Mr REvel.
Cyril Bonnet, a journalist at Nouvel Observateur, the news magazine, said the row was a "remarkable illustration of the Streisand effect" - so called because Barbara Streisand's attempt to block photographs of her Malibu residence in 2003 ensured that they were seen by even more people.
Slate, a French internet site, launched a competition to find the best caption for photograph of Mr Hollande.
"This year, the teacher is called Obama," says one. "It's not my fault," says another. "How am I going to tell them that they will have to retire at 80," says a third.
Behind the jokes, however, lay an awkward controversy for AFP, which is officially independent but unofficially reliant on French public authorities which subscribe to its news wires.
A recent report said that €114 million (£96 million) of AFP's annual income of €281 million in 2011 came in the form of subscriptions from the French public sector. Critics say this is a disguised subsidy, which is denied by AFP.
It's not the way a person looks that defines if they are an idiot or not, it is the way they act. So, I guess we already know the answer to that one.