International Monetary Fund chief Christine Lagarde is facing questions at a special Paris court on Thursday over a controversial financial deal that she oversaw as French Finance Minister.

The 2008 arbitrage deal handed about €400 million ($520 million) to magnate Bernard Tapie to settle a dispute with state-owned bank Credit Lyonnais over the botched sale of Adidas in the 1990s.

Mr. Tapie was close to then-French President Nicolas Sarkozy, who was Ms. Lagarde’s boss. Critics have said the deal was too generous to Mr. Tapie at the expense of the French state, and that the Adidas case shouldn’t have gone to a private arbitration authority because it involved a state-owned bank.

More broadly, the deal was seen by many as an example of the cozy relationship between big money and big power in France. And the case threatens to sully the reputation of Ms. Lagarde, who has earned praise for her negotiating skills through Europe’s debt crisis and is seen as a trailblazer for women leaders.

Ms. Lagarde, smiling at reporters, left her Paris apartment Thursday morning and appeared at a special court that handles cases involving government ministers. She has denied wrongdoing.

Investigators opened an inquiry in 2011 into possible charges of “complicity to embezzlement of public funds” and “complicity to forgery.” The probe may not result in a trial. If it does, and if Ms. Lagarde were to be convicted, she could face up to 10 years in prison, according to prosecutors.

She and the Washington-based IMF were aware of the probe when she took over as Managing Director from Dominique Strauss-Kahn in 2011. The IMF has expressed its confidence in Ms. Lagarde throughout the investigation.

In March, French investigators searched Ms. Lagarde’s Paris home. Her lawyer said at the time that Ms. Lagarde welcomed the search as a step toward proving her innocence.

French Finance Minister Pierre Moscovici told Le Monde that the government may seek to annul the arbitration deal if enough evidence emerges of wrongdoing.

Mr. Tapie, a tycoon and former football club owner who has served as an actor, singer and government minister insists that he deserved the settlement. He says the investigation into the deal is “bogus,” and a politically motivated hunt by the governing Socialists against Mr. Sarkozy’s conservatives.

“Lagarde’s fate doesn’t concern me,” Mr. Tapie said on Europe-1 radio on Thursday. “When evidence is discovered, then we’ll talk.”

Mr. Tapie himself may be targeted in a separate probe.

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