Though not accused of financially profiting from the case herself, Lagarde has been accused of being complicit in the mis-spending of public funds by allowing the legal dispute to go to arbitration against the recommendation of advisers within the French finance ministry.
Three prosecutors at the court specializing in cases against former government ministers will question Lagarde to see whether she over-stepped her authority and whether she took the decision herself or was instructed to do so by Nikolas Sarkozy.
The case against her could either be dropped or Lagarde could be placed under formal investigation, according to Reuters.
If convicted, Lagarde could receive a fine of up to 150,000 euros and up to ten years in jail.
She has repeatedly denied any wrongdoing but if a formal investigation were to be started, it could make her position as head of the IMF uncomfortable. In March, Lagarde's apartment in Paris was searched by investigators.
The IMF's executive directors said on Thursday they remained confident that Lagarde could do her job despite the court case.
The Lagarde case could have far-reaching ramifications on a French public already disaffected with its politicians, Douglas Webber, professor of political science at France's leading business school, INSEAD, told CNBC on Thursday. France's current government already facing scrutiny and public unpopularity after a minister was found to have hidden money in a Swiss bank account.
"If she were to be 'charged' in respect of this accusation, it may not necessarily have a significant and direct impact on her own career, but it will reinforce increasingly widespread sentiments in France that the country's political elite is corrupt and self-seeking and strengthen already growing support for the political extremes, especially Marine Le Pen's Front National," Webber said.
Reuters contributed reporting to this story.
- By CNBC's Holly Ellyatt, follow her on Twitter