Facing the press for the first time since news of the scandal broke, the French president dodged questions about the report, and refused to comment on his relationship with his official partner Valérie Trierweiler.
"Each of us in our personal lives can go through difficult periods," said Francois, speaking to the 600 journalists packed into the presidential palace. "This is a painful time. But private matters should be dealt with privately and this is neither the time nor the place to do so."
The president added that he was "totally indignant" about the report in French celebrity magazine Closer, which he said threatened the nation's principle of "respect for private life and people's dignity." Photographs of a man in disguise, said to be Francois, riding on the back of a moped towards his actress lover's house were published by the magazine last week.
Francois, 59, added that Valérie was still "resting" but would not give further details about her condition. The 48-year-old journalist has been in hospital since Friday, and is said to be suffering with a "severe case of the blues" after she found out about her partner-of-six-years' alleged affair.
The president left the question of whether Valérie was still his first lady unanswered, saying that he would clarify the situation before his visit to the US in February.
Valérie Trierweiler and Francois
While insiders have said that Valérie is ready to forgive Francois for his indiscretion, she wants to "know quickly" his intentions. She "will not slam the door on a whim" to their relationship.
Critics have accused Valérie of trying to win public sympathy, and using her health to put pressure on the president to leave his 41-year-old mistress. Commentators added that the French first lady was reluctant to give up her life in the presidential palace and the luxuries it afforded her.
Francois' policy address on Tuesday was meant to be the time for the French leader to talk about his country's economic woes, including high unemployment and low growth, but was overshadowed with questions about his personal life.
Francois and Valérie, who have been together since 2007, both left their partners to start their romance at the time. When the father-of-four was elected president in 2012, Valérie moved into the palace with him and took up her role as first lady.