Hollande reacted furiously to the allegation -- backed up by photos reportedly showing the president entering the flat of actress Julie Gayet -- but did not deny it, threatening legal action over what he called an attack on his right to privacy.
Closer's Friday edition carried a seven-page report on the 59-year-old president's alleged infidelity under the headline "Francois Hollande and Julie Gayet - the president's secret love".
To back up its claims, the magazine printed photos of Gayet, 41, arriving at a flat in an upmarket part of Paris on December 30, not far from the Elysee palace where Hollande lives.
Half-an-hour later, a man whom they identify as Hollande's bodyguard inspects the hallway of the apartment block before the arrival of a scooter with two helmeted men on board, one of whom they say is Hollande -- although his face is never revealed.
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The alleged bodyguard, however, does show his face and is identified as part of Hollande's official security detail.
Three hours later, a helmeted man is pictured mounting a chauffeur-driven scooter under the eyes of the alleged bodyguard.
Speaking in a personal capacity, Hollande slammed the report as an attack on the right to privacy, to which he "like every other citizen has a right".
The president, in a statement released to AFP, said he was "looking into possible action, including legal action," against the weekly magazine. But he did not deny the allegations.
In December, French actor Stephane Guillon made innuendos on the subject during a talk show where he and Gayet were invited to promote a film in which they co-star.
When the host asked Gayet about her public support for Hollande, Guillon -- sitting next to her -- started laughing. Asked why, he stuttered and finally said: "He would come on set. The president likes the film, his wife much less."
Hollande lives with his partner Valerie Trierweiler, a journalist for whom he left fellow Socialist politician Segolene Royal, the mother of his four children.