Despite the rumors, one of the few journalists to point to them when Mr. Strauss-Kahn was appointed to the fund was Jean Quatremer, the Brussels correspondent for Libération. He wrote on his blog that Mr. Strauss-Kahn’s “only real problem” was his “rapport” with women. “Too insistent, he often comes close to harassment,” he wrote. “A weakness known by the media, but which nobody mentions. (We are in France.) The I.M.F., however, is an international institution with Anglo-Saxon morals. A misplaced gesture, a too specific allusion, and it will be a media scramble.”

Image Mr. Strauss-Kahn’s absence would help the candidacy of François Hollande, top, and might encourage Martine Aubry, middle, to run. Ségolène Royal, above, will also run. Credit... From top: Jacques Demarthon/Agence France-Presse -- Getty Images; Yiorgos Karahalis/Reuters; Stephane Mahe/Reuters

Mr. Strauss-Kahn behaved aggressively toward a young female journalist and novelist, Tristane Banon, in 2002, according to the newspaper Le Parisien and other Web sites, and corroborated by Ms. Banon herself in a 2007 television interview on Paris Première, a cable channel. At the time, she said that a French politician — whom she later said was Mr. Strauss-Kahn — had tried to rape her in an empty apartment in Paris after she had contacted him for a book she was writing.

“He wanted to grab my hand while answering my questions, and then my arm. We ended up fighting, since I said clearly, ‘No, no.’ We fought on the floor, I kicked him, he undid my bra, he tried to remove my jeans,” she said.

Afterward, she said that she had contacted a well-known lawyer who already had “a pile of files on Mr. Strauss-Kahn,” but that she never filed a complaint. “I didn’t dare; I didn’t wish to be the girl who had a problem with a politician for the rest of my life,” she said.

Her mother, Anne Mansouret, a Socialist, later confronted Mr. Strauss-Kahn and asked why he had attacked her daughter, she told Rue 89, an online newspaper. According to her, he responded: “I don’t know what happened, I went crazy.”

At the Institut d’Études Politiques de Paris, known as Sciences Po, where he was an economics professor, “he had a real power of attraction,” said a former student in an interview. “There were always hordes of female students waiting to talk to him at the end of his classes,” she said, speaking on the condition of anonymity.

Well before Mr. Strauss-Kahn’s arrest there had been reports that Mr. Sarkozy was gathering information to discredit Mr. Strauss-Kahn should he run for president. In a famous incident, reported by the news magazine Le Point, Mr. Strauss-Kahn confronted Mr. Sarkozy in the men’s room at the Group of 20 summit meeting in Pittsburgh in September 2009, saying: “I’ve had more than enough of this continued gossip about my private life and about supposed dossiers and photos that could come out against me. I know that this is coming from the Élysée. Tell your guys to stop or I’ll go to the courts.”