The gossip magazine also printed more details of the alleged romance, which it says began during the 2012 presidential race.
Julie Gayet has announced she is suing Closer magazine for breach of privacy.
Francois Hollande’s official partner and France’s first lady, Valerie Trierweiler, remains in hospital, where she was admitted after learning of the alleged affair a week ago.
In its latest revelations, Closer said Francois Hollande used a second apartment in the west of Paris to meet the 41-year-old actress.
It is claimed the pair snatched weekends together in the south of France, and that Francois Hollande made excuses to avoid a holiday in Greece last year with Valerie Trierweiler, so he could travel instead to his Correze constituency with Julie Gayet.
The magazine said the president and Julie Gayet had been having a “turbulent romance” for two years – during and after Francois Hollande’s election campaign.
The magazine did not publish any further photos despite earlier reports that it would.
Julie Gayet is seeking 50,000 euros ($68,000) in damages and 4,000 euros in legal costs from the magazine.
If she wins, Closer will have to publish the legal verdict on its cover page, AFP reports.
Francois Hollande decided not to take legal action after first threatening to.
Valerie Trierweiler – seemingly still keen to defend Francois Hollande’s character – is said to have defended him following reports he had not visited her in hospital.
She phoned a journalist on Thursday to explain it was her doctors who had asked Francois Hollande not to attend.
Valerie Trierweiler said she is still too weak to stand – and that the president has sent flowers and chocolates in his absence.
In response to the reports, a source at the Elysee Palace said Francois Hollande was “not unhappy” about the hospital forbidding him to visit.
Meanwhile, French magazine Le Point has quoted a friend of Valerie Trierweiler saying she had not tried to commit suicide but had taken “one pill too many”.
Francois Hollande, 59, told reporters on Tuesday he was experiencing a “difficult moment” in his private life but refused to answer questions over the report in Closer, saying “private matters should be dealt with privately”.
Nor would he clarify whether Valerie Trierweiler, 48, was still first lady before a February trip to the US.
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