Valerie Trierweiler was admitted to hospital, apparently in shock after learning of the reports.
Closer magazine first published details of Francois Hollande’s link with Julie Gayet last Friday.
The gossip magazine has further alleged that the affair began during the 2012 presidential race.
Julie Gayet, 41, says she is suing Closer magazine for breach of privacy, seeking 50,000 euros ($68,000) in damages and 4,000 euros in legal costs.
Francois Hollande visited his partner in hospital for the first time on Thursday evening, the Elysee Palace confirmed on Friday, without giving further details.
Valerie Trierweiler, 48, was admitted to hospital last Friday – hours after the first revelations made by Closer magazine.
In an apparent defense of Francois Hollande’s character, Valerie Trierweiler reportedly spoke to a radio journalist earlier on Thursday to explain that he had been told to stay away from the hospital by doctors.
The journalist said she was told Francois Hollande had sent flowers and chocolates and had met the team that is looking after Valerie Trierweiler.
Valerie Trierweiler said she was “very tired to the point of not being able to stand up”, and had been suffering from low blood pressure and low morale but was determined to leave hospital with her head held high.
In response to the reports, a source at the Elysee Palace said Francois Hollande was “not unhappy” about the hospital forbidding him to visit.
French media have claimed that Valerie Trierweiler suffered an anxiety attack last week, but her friends have played down her condition.
Le Point magazine quoted a friend of Valerie Trierweiler as saying she had taken “one pill too many”, but had not tried to commit suicide.
At his annual news conference on Tuesday at the Elysee to discuss his political agenda, Francois Hollande was asked questions about the alleged affair.
Francois Hollande, 59, said 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 was still first lady before a February trip to the US.
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