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© Valery Hache/AFP/Getty ImagesFrench actor Julie Gayet and President François Hollande, who are alleged to be having an affair.
French president says he deplores attack on privacy by Closer magazine, which published alleged images of him visiting actor

The French president, François Hollande, has threatened legal action over claims he is having an affair with an actor.

The glossy celebrity magazine Closer published a special edition on Friday including a seven-page report on the leader's alleged relationship with Julie Gayet.

In a statement from the Elysée Palace, Hollande did not directly deny the report but accused the magazine of breaching his privacy. He said advisers were looking at what action to take against the magazine, which caused a storm in 2012 after publishing paparazzi photographs of the topless Duchess of Cambridge on a private holiday in the south of France.

The statement said Hollande "deeply deplores the attacks on the principle of respect for privacy, to which he, like every citizen, has a right".

Closer published photographs showing a man in a motorcycle helmet outside what it said was Gayet's Paris apartment, along with a man reported to be the president's bodyguard.

Hollande's partner is the former Paris Match journalist Valérie Trierweiler who is considered to be France's first lady. He has four children with the politician Ségolène Royal, who ran against Nicolas Sarkozy in the 2007 presidential race.

In March last year, Gayet, 41, began legal action to identify who was behind internet rumours that she was romantically involved with the president.

During Hollande's 2012 election campaign she took part in a political broadcast in which she described the presidential candidate as "humble", "incredible" and a man who "really listens".

In the past, the French media have been considerably more circumspect about the love lives of the country's leaders, who have taken refuge behind the country's strict privacy laws.

For many years, the last Socialist president of France, François Mitterrand, led a double life with his wife, Danielle, and lover, Anne Pingeot, with whom he had a daughter, Mazarine. Although the existence of Mitterrand's second family was an open secret, nothing was ever published until Paris Match obtained photos of Mazarine, then aged 20, and got the president's permission to publish them.

The Closer story provoked a storm on Twitter, coming just hours after the banning of a show by the controversial comedian Dieudonné M'Bala M'Bala, and the announcement that La Redoute, a mail order company, was laying off hundreds of staff.