Lagarde to Appear in French Court PARIS - Christine Lagarde, the head of the International Monetary Fund, will soon learn if she must face a full criminal investigation over her role in a contentious financial deal that dates back to her time as French finance minister. Ms. Lagarde, the fund's managing director since 2011, was set to appear Thursday for a hearing before the Court of Justice, which handles cases involving the actions of ministers and former ministers in the performance of their duties, said Christopher L. Baker, a lawyer who represents Ms. Lagarde. According to unsourced reports Wednesday in the French media, including the daily newspaper Le Monde, the three judges on the court are leaning toward placing Ms. Lagarde under formal investigation on suspicion of being accessory to fraud and the misuse of public funds. At issue is Ms. Lagarde's involvement in the adjudication of a long-running dispute in which Bernard Tapie, a colorful and controversial businessman-politician with ties to the former president, Nicolas Sarkozy, had accused Crédit Lyonnais, a state-owned bank, of defrauding him and looked for compensation in the courts. Ms. Lagarde, Mr. Sarkozy's finance minister from 2007 to 2011, allowed the case to go to an arbitration panel that awarded Mr. Tapie, formerly the owner of Adidas and the Olympique Marseille soccer team, a settlement of €403 million, or about $518 million at current exchange rates. Critics, particularly on the left, have argued that the award was overly generous to Mr. Tapie and suggested that the businessman - who had been a Socialist but began backing Mr. Sarkozy's center-right Union for a Popular Movement in 2007 - had benefited from special treatment. Ms. Lagarde denies any wrongdoing in the case. Investigators are seeking to understand her role in the arbitration decision and to answer the question of why she did not try to overturn it. The hearing could last into Friday, Mr. Baker said. In the French legal system, there is no certainty that those placed under formal investigation will ultimately face trial, nor are they presumed guilty. While the designation does suggest that investigators believe they have solid grounds for suspicion, Le Monde reported that they were also reserving the possibility of assigning to Ms. Lagarde the status of "assisted witness," still obliging her to answer investigators" questions, but without the opprobrium attached to a formal investigation. Ms. Lagarde has never been accused of profiting personally from the affair, and she and her lawyers have said they welcome the chance to tell her side of the story. Mr. Baker said Ms. Lagarde "took a decision to put an end to 15 years of litigation, and did so in a manner that was both prudent and legal and in the best interest of the state." "We have no reason to believe this will go to trial," Mr. Baker added. The I.M.F. board was informed of the case before Ms. Lagarde became managing director, and in March it "expressed its confidence that Madame Lagarde would be able to effectively carry out her duties." Still, the legal uncertainty a formal investigation would bring could complicate Ms. Lagarde's life at the fund. If she were to step down, she would be the second consecutive French leader of the I.M.F. to be felled by scandal: The career of Dominique Strauss-Kahn, Ms. Lagarde's immediate predecessor at the institution and once a Socialist contender for the French presidency, was destroyed in 2011 by accusations that he sexually assaulted a housekeeper in a New York hotel. The International Monetary Fund did not immediately reply to requests for comment. President François Hollande's government may seek to have the arbitration result annulled if Ms. Lagarde is placed under formal investigation, Le Monde quoted Finance Minister Pierre Moscovici as saying Wednesday. But Mr. Moscovici said Ms. Lagarde "still has the confidence of the state authorities."