The arbitration payment was made to a supporter of France's former president Nicolas Sarkozy.
Lagarde risks being placed under formal investigation at the hearing for her 2007 decision as Sarkozy's finance minister to use arbitration to settle a long-running court battle between the state and high-profile businessperson Bernard Tapie.
Under French law, that step would mean there exists "serious or consistent evidence" pointing to probable implication of a suspect in a crime.
It is one step closer to trial but a number of such investigations have been dropped without any trial.
Such a move could prove uncomfortable for the International Monetary Fund, whose former head, Frenchman Dominique Strauss-Kahn, quit in 2011 over a sex assault scandal, and for a woman voted the most influential in France by Slate magazine.
"It's a pleasure to see you," a smiling Lagarde said to reporters as arrived at the Paris court for a hearing that could last into Friday.
Misuse of funds
She is not accused of financially profiting herself from the payout and has denied doing anything wrong by opting for an arbitration process that enriched Tapie.
With interest, the award amounted to €403-million.
However a court specialising in cases involving ministers is targeting her for complicity in the misuse of funds because she overruled advisers to seek the settlement.
Sources close to the IMF board have said they are not worried by the affair and are confident Lagarde herself did not profit from it.
But they added the board might review its position if judicial procedures took her away from her duties.
Tapie, a one-time Socialist minister who later became a supporter of the conservative Sarkozy, said the bank defrauded him after it later resold his stake for a much higher sum.
Credit Lyonnais, now part of Credit Agricole, has denied any wrongdoing.
Current Finance Minister Pierre Moscovici told Le Monde newspaper Lagarde retained the support of France's government, but said that it would appeal against the arbitration award if she was placed under formal investigation. – Reuters