PARIS — A sex scandal is the last thing France’s president needs.

Three-quarters of the French already think Francois Hollande is doing a lousy job of running the world’s No. 5 economy. And now a big policy address Tuesday is sure to be overshadowed by personal troubles so awkward that even the famously blase French can’t ignore them.

His first lady, journalist Valerie Trierweiler, is hospitalized because of a tabloid report that Hollande is having an affair with a somewhat recognizable French actress. Trierweiler may remain in the hospital for six to eight days to recover from the “very strong emotional shock,” her chief of staff said Monday.

Hollande is a lifelong bachelor, though he has four children with former presidential candidate Segolene Royal. He and Trierweiler have lived together since 2007, and while they’re unmarried, Trierweiler occupies the so-called “madame wing” of the presidential palace, travels abroad with Hollande and functions as the first lady.

The French public initially shrugged off talk about the secret affair as Hollande’s private business. But pollsters said Monday that Trierweiler’s hospitalization renders the scandal more serious, and is likely to damage Hollande’s already-record-low popularity ratings.

“Today, we have a victim, in the person of Valerie. This could create growing empathy for Valerie and hurt the image of Hollande, who could be perceived as the cause of Valerie’s unhappiness,” said Yves-Marie Cann of the CSA polling agency. “And that could weigh on the image that Hollande has had of someone nice and honest.”

Patrice Biancone, chief of staff to Trierweiler, vigorously denied Internet rumors that she had attempted suicide, and said she simply needs rest. Asked about her plans, he told The Associated Press: “When you are in a situation like this, you can’t think about tomorrow, you can’t think with lucidity.”

That puts even more pressure on Hollande to come out with a forceful new economic policy when he faces a New Year’s news conference Tuesday.

While the French often say they don’t care about their leaders’ private lives, readers quickly cleared out kiosks of the magazine Closer when it published images last week of what it said was a helmeted Hollande secretly visiting actress Julie Gayet.

Hollande threatened legal action over what he said was an invasion of his private life, and Gayet has not commented publicly.

French voters are “intrigued and interested, but don’t want this to distract him from the real problems of jobs, the deficit,” said Emmanuel Riviere of the TNS-Sofres polling agency.

Many French want Hollande to clarify who his first lady is – and then get back to the business of fixing the flagging economy.

The role of first lady in France is not as important as its American counterpart, but “retains an importance in the collective imagination of the French people” because she is seen as “France’s image to the world,” Cann said.