His partner, journalist Valerie Trierweiler, has been in hospital since Friday when a magazine published photographs it said proved Mr Hollande's liaison with actress Julie Gayet, heaping new pressure on the already unpopular leader.
He was asked following a major economic policy speech yesterday whether Ms Trierweiler remains the first lady. In his first comments since the magazine report, he responded: "Everyone in his or her personal life can go through ordeals - that's the case with us."
Mr Hollande said his "indignation is total" over the report, calling it a "violation that touches a personal liberty". He did not deny the report.
The latest revelations call into question whether a complex personal life can be private for someone with round-the-clock bodyguards and raise questions about the role of France's First Lady. Ms Trierweiler is the first person to hold the post who was not married to the president.
Mr Hollande said he will clarify who the First Lady is before he takes a trip to the US next month but would not comment further yesterday. He said state funds spent on the First Lady should be made public and be "as small as possible". The First Lady does not have formal status in France, but in practice they have an office in the presidential palace and staff.
The pictures published in Closer included one of a man said to be Mr Hollande being ferried by motorcycle to an apartment where Ms Gayet waited.
The issue even reached the floor of parliament. A leading member of the opposition conservative UMP party accused the president of taking unreasonable risks with his security.
Asked whether his security was compromised, Mr Hollande said, "My security is assured everywhere, and at any moment.
"When I travel officially and when I travel on a private basis, I have protection that is less suffocating. But I am protected everywhere."
He left open the possibility of suing Closer over invasion of privacy.
Photographer Sebastian Valiela said he was surprised at the lack of security for Mr Hollande whose government has been repeatedly threatened by al Qaeda.
He said: "To go to the rendezvous with Julie Gayet, he was taking some risks. As soon as he got into the apartment, his guards left."
Twenty years ago Valiela rocked France's political establishment with images that revealed the secret family of then-president Francois Mitterrand, showing the Socialist leader emerging from a restaurant with the daughter he had never acknowledged.
Francois Rebsamen, a Socialist MP and one of Mr Hollande's friends, said the recent revelations showed the entire idea of a First Lady was obsolete.
He said: "Francois Hollande himself said it at one point: You elect a person. And then this person can live alone, can be single, can live with another man or a woman. It's no one's business and it doesn't come into play."
Mr Hollande, who has four children from a previous relationship with a leading politician, was elected in a backlash against his flamboyant predecessor Nicolas Sarkozy.