French actress Julie Gayet and President Francois Hollande
French President Francois Hollande told AFP on Friday he was considering legal action against Closer after the magazine said he was having an affair with an actress.
Speaking in a personal capacity, Hollande condemned the coverage as an
"attack on the right to privacy," to which he "like every other citizen has a right".
Hollande told AFP in a statement he was "looking into possible action, including legal action," against the weekly magazine.
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".
Closer, echoing reports published on various websites in recent days, said Hollande routinely drives through Paris on his scooter to spend the night with his 41-year-old mistress.
"Around New Year's Day, a helmeted head of state joined the actress at her apartment, where he has got into the habit of spending the night," Closer wrote on its website.
Respected news weekly L'Express had last month reported that the presidential palace's security services were increasingly concerned by Hollande's frequent "escapades".
Closer said the pictures raised security concerns by showing that the head of state is accompanied by only one bodyguard when he treks halfway across Paris to Gayet's flat.
The bodyguard "even brings the croissants", Closer said.
Hollande lives with his partner Valerie Trierweiler, a journalist for whom he left fellow Socialist politician Segolene Royal, the mother of his four children.
Gayet, who appeared in one of Hollande's 2012 election commercials, filed a complaint in March over rumours of the affair which she said were a breach of privacy.
Gayet, a mother of two, is an established television and cinema character actress who has appeared in more than 50 films.
She had a leading part in "Quai d'Orsay", a 2013 satirical film centred on the French foreign ministry. Her filmography also includes the titles "Shall We Kiss?" and "My Best Friend".
In December, French actor Stephane Guillon made repeated innuendos on the subject during a talk show where he and Gayet were invited to promote a film in which they co-star.
She appeared a little uneasy but laughed with him when he said Hollande had been visiting the film set and quipped that Trierweiler was less enthusiastic about the film than Hollande.
If confirmed, Hollande's relationship with Gayet would perpetuate a long French tradition of philandering presidents and senior politicians.
Former president Jacques Chirac is believed to have had many extra-marital conquests, as did his predecessor Francois Mitterrand, who even had a daughter born to a mistress.
Valery Giscard d'Estaing was also described as an incorrigible womaniser. He hinted in a recent book at an affair with Princess Diana.
France's media is subject to strict laws on privacy, and has in the past drawn a veil over rumours about the personal lives of the country's leaders.
However, the French are known for being tolerant of their leaders' infidelities, which have in the past proved to have little or no negative impact on popularity ratings.
A survey released on Thursday -- before the latest allegations -- showed that only 23 percent had a positive opinion of Hollande's performance as president.