PARIS — Since taking over in May , Francois Hollande has repeatedly asked the French to regard him as a “normal” president.

Well, maybe. But it would be easier if his first lady, Valerie Trierweiler, were not a live-in girlfriend.

It would also be easier if he had married the woman he lived with for nearly three decades and had four children with before taking up with Trierweiler, a political reporter who wants to carry on as an independent journalist with an office near the president’s. And it would certainly be easier if the two women were not the subject of several books just out that describe in shudder-inducing detail how they elbowed for prominence as Hollande rose to the presidency.

“For a president who wants to be normal, this is not a great record,” said Philippe Allary, a physical therapist who prefers former president Nicolas Sarkozy.

The public airing of Hollande’s family troubles — one reviewer wondered whether to describe them as “vaudeville or tragedy” — has undercut the president’s standing, according to his son; his former companion, Segolene Royal; and independent analysts, because it depicts him as unable to impose his will on two obviously headstrong women who cannot stand each other.

“This is being integrated into the general perception of Hollande, that he is unprepared to be president,” said Nicole Bacharan, a researcher associated with the Political Science Institute in Paris. Hollande’s reputation as indecisive and afraid of confrontation was set aside in the euphoria of his election, she noted, “but now it is coming back with a vengeance.”

France has long been known as a country that tolerates romance and extramarital sex in a way that would be impossible in U.S. politics. But in the past half-dozen years, it has been treated to a string of soap operas at the pinnacle of power that, in the eyes of many observers, have permanently shattered the barriers that long separated private and public lives in France.

After first ladies who stood solidly behind presidents Charles de Gaulle, Georges Pompidou, Valery Giscard d’Estaing, Francois Mitterrand and Jacques Chirac, Sarkozy opened the door to “Dallas” as he won the presidency and took office in 2007. More or less publicly, he was at the time struggling to prevent his second wife, Cecilia, a former model, from running off with a buttery-smooth event planner.

He failed, and Cecilia left for a new life in New York. Within weeks of moving into the Elysee Palace, however, Sarkozy met Carla Bruni Tedeschi, another ex-model. After a swift courtship that included much-photographed excursions to Disneyland Paris and the ruins of Petra in Jordan, they were married, and the willowy Carla became a celebrity first lady — and later a celebrity mother.

Then came Dominique Strauss-Kahn, the Socialist Party luminary and International Monetary Fund chief who was widely rated as the candidate who would shoot down Sarkozy in the 2012 election. But that was before he was arrested in May 2011 over allegations of sexual assault in a New York hotel room.