Valerie Trierweiler had been expected to leave hospital on Monday, but her aides said doctors had told her she needed more rest.
France’s first lady went to hospital on Friday shortly after Closer magazine alleged Francois Hollande was having an affair with film actress Julie Gayet.
Francois Hollande did not deny the report but protested at invasion of his privacy.
The president and Valerie Trierweiler have been together since 2007.
A presidential news conference scheduled for Tuesday on plans to boost the flagging economy now looks likely to be overshadowed by Francois Hollande’s private life, correspondents say.
Opinion polls already suggest he is one of the most unpopular French presidents ever.
Aides of Valerie Trierweiler, who is Francois Hollande’s official partner and lives at the Elysee Palace, said she went to hospital on Friday for “rest and some tests”.
On Monday, an aide told Europe 1 broadcaster: “The doctors will determine when she can be dismissed from hospital. She needs to recover from the shock she has suffered.”
Le Parisien newspaper quoted one of Valerie Trierweiler’s friends as saying she is willing to forgive Francois Hollande, but wants to know about his intentions as soon as possible.
The French media face strict privacy laws, but the tradition of secrecy over the private lives of public figures has been steadily eroded in recent years.
On Friday, Closer magazine printed a seven-page article about the alleged affair between Hollande Hollande and Julie Gayet.
The article was illustrated with photos showing a man said to be the president visiting a flat near the Elysee Palace at the same time as Julie Gayet.
Francois Hollande, who has never married, left his previous partner – fellow Socialist politician Segolene Royal – to be with Valerie Trierweiler.
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