PARIS – France’s president is reported to be sneaking around on a motorcycle to have a secret affair with actress Julie Gayet.

But who takes the brunt of the heat? In a very French twist, it’s increasingly looking like his apparently jilted first lady, who has been hospitalized since she found out.

The question on many French lips this week is not “How could François Hollande have done such a thing?” but rather “Do we really need a first lady?”

That’s in part a reflection of a French willingness to forgive infidelity by men in public office, regardless of the damage it causes to their women.

And it’s in part because the French have never fully embraced Valérie Trierweiler, a journalist who has been living with Hollande since he split with the mother of his four children in 2007.

Seen as cold and distant, Trierweiler has followed Hollande on international visits and played the role of first lady but, unlike her predecessor Carla Bruni, has failed to capture the hearts of the French public. Trierweiler and Hollande are not married, and his reported affair is shining a new spotlight on the nearly $27,000 in taxpayer money spent each month on the first lady’s staff and office in the presidential palace.

If Trierweiler’s not the president’s favorite anymore, the logic goes, why should she get to keep the perks?

Never mind that she has been hospitalized for nearly a week for what her aides call “very strong emotional shock.” She reportedly said the news of Hollande’s dalliances hit her like a high-speed train.

At a major news conference Tuesday, Hollande confidently brushed off questions about an affair by saying it’s private – and the French media and public have so far seemed happy to leave it at that.

Compare that to the experience of U.S. President Bill Clinton in the 1990s. The scandal over his relationship with intern Monica Lewinsky dominated headlines for months and led to his impeachment for lying to investigators, for which he was acquitted. His wife, Hillary Rodham Clinton, was generally seen to have come out stronger from the scandal, and her political career flourished.

Wednesday, many French people seemed ready to move on, just five days after the tabloid report about a late-night rendezvous between Hollande and Gayet around the corner from the president’s Élysée Palace.

Hollande’s private life “shouldn’t be publicly discussed,” said Paris resident Jean-Paul Lechevalier. “He is a man like others. What is more interesting are his announcements to win back the battle for the economy.”

Emmanuel Riviere of the TNS-Sofres polling agency said that attitude is typical. “The French are not too severe with the idea that political leaders could have liaisons outside marriage, as long as it doesn’t impact the course of political action,” he said.

He added that some French people “will say that a president who is a (sexual) conqueror, who has the ability to seduce, will be more accepted.”

Hollande is the latest in a line of French leaders with complicated private lives. François Mitterrand had a secret daughter with his longtime mistress. Valéry Giscard d’Estaing reportedly crashed his car en route to a liaison with his lover. Nicolas Sarkozy was the first French president to divorce, date and remarry in office.