Christine Lagarde, I.M.F. Chief, Is Found Guilty of Negligence

The case against Ms. Lagarde centered on Bernard Tapie, a former entertainer and owner of Adidas who had previously been jailed on corruption charges. Mr. Tapie accused the lender Crédit Lyonnais, in which the French state had a stake at the time, of cheating him when it oversaw the sale of his share in the sportswear empire in 1993. Years of costly legal battles ensued.

In 2007, Ms. Lagarde sent the dispute to a three-person private arbitration authority that awarded Mr. Tapie more than 400 million euros, or $420 million at current exchange rates, in damages and interest, to be paid by the state.

Her critics said that decision was politically tainted, and she was charged with negligence for allowing the arbitration and for then declining to appeal the panel’s verdict.

The trial against Ms. Lagarde was just one facet of the scandal — many people associated with it are under investigation, for accusations as varied as embezzlement and organized fraud.

Legal proceedings are expected to begin next year against Stéphane Richard, the chief executive of the French telecommunications giant Orange and the former chief of staff to Ms. Lagarde, who said that she had relied on his judgment to send Mr. Tapie’s case to arbitration.

Mr. Tapie, who has been ordered by a French court in 2015 to repay the full amount with interest after a judge invalidated it, is expected to be called to a separate trial. He is under bankruptcy protection and has not repaid the sum.

Separately, a judge on the arbitration panel that heard Mr. Tapie’s case is accused of fraud and is expected to be tried, as is Mr. Tapie’s lawyer.

Witnesses at Ms. Lagarde’s trial described a system in which influential, wealthy members of the French elite, like Mr. Tapie, had easy access to government officials and parlayed those relationships to the advantage of both parties, sometimes at the expense of taxpayers.

Bruno Bézard, a former director of the French Treasury, described “curious relationships” at the Finance Ministry when he worked there with Ms. Lagarde, saying that Mr. Tapie was often seen walking around the hallways, presumably to visit officials — “which was rather unexpected.”

Mr. Bézard, who led a government body overseeing state holdings, including a bank set up to take over Crédit Lyonnais’ bad assets, said Ms. Lagarde had ignored repeated warnings from members of his staff not to proceed with arbitration.

“It was the worst of solutions,” he said. “But we quickly learned that a political decision had been made, despite the colossal risks” that the state would have to pay for any damages and interest awarded to Mr. Tapie.

Mr. Bézard suggested that Ms. Lagarde had further erred by not challenging the amount of the payout.

“I was more shocked by the speed with which we gave up on contesting it than by the speed of the arbitration decision,” he said. “Given that the amount was so scandalous, even if we had one chance in 1,000 to win, it should have been done.”

Ms. Lagarde testified that she had declined to do so because it could have resulted in a slew of new lawsuits from Mr. Tapie and additional costs to the state.

Mr. Tapie, a former Socialist who served in the administration of President François Mitterrand in the 1990s, switched political allegiances and in 2007 backed the presidential campaign of Nicolas Sarkozy — the president at the time of the arbitration hearing.

Mr. Tapie visited the Élysée Palace, the seat of the French presidency, at least 20 times during Mr. Sarkozy’s first two years in office, the French news media reported. The businessman is said to have met with Mr. Sarkozy and François Fillon, the prime minister at the time and the front-runner in next year’s presidential election.

In July 2007, Mr. Tapie met with Mr. Richard, Ms. Lagarde’s chief of staff, and Claude Guéant, an aide to Mr. Sarkozy.

Mr. Richard, also a longtime friend of Mr. Sarkozy’s, later said that he had paved the way to move the case to arbitration because he left the meeting with the “strong impression” that it is what Mr. Guéant favored.

Mr. Richard refused to testify at Ms. Lagarde’s trial, citing a parallel criminal inquiry into his role in the events. Mr. Guéant was questioned in 2014 as part of a separate investigation into the matter. Both men have denied any wrongdoing.