Reuters Business Report - She's used to answering questions at high-profile press conferences in her current role as head of theInternational Monetary Fund.
Her role in a multi-million euro payment made to a supporter of former French President Nicolas Sarkozy is under investigation.
Back in 2007, when Lagarde was Sarkozy's finance minister, she decided to use arbitration instead of a court hearing to settle a dispute between the state and French businessman Bernard Tapie.
Lawyer Christopher Mesnooh explains the investigation.
"The final arbitration award had allocated more than 400 million euros to Mr. Tapie in the form of different damages, both monetary and moral harm, and there are many people within the French government who believed that the recourse to arbitration or private justice was not appropriate."
Lagarde's Paris apartment was searched by French authorities in March.
She isn't accused of financially profitting herself from the payout made to Tapie.
She spoke about the so-called Tapie affair in 2011, when she was still finance minister.
Christine Lagarde, Then French Finance Minister,
"We are in a democracy, obviously I want all these questions to be clarified. I have every confidence in this procedure, not least because my conscience is perfectly clear."
Lagarde risks being placed under formal investigation when the hearing wraps up on Friday.
Under French law, that could bring the investigation closer to trial.
That move could be uncomfortable for the IMF - especially after its former head, Frenchman Dominique Strauss-Kahn, quit in 2011 over a sex scandal.
The Washington-based IMF is standing by Lagarde and has reaffirmed its confidence in her.