What are the charges?
Lagarde is accused of approving an out-of-court settlement to Bernard Tapie, a business tycoon, during her term as finance minister under Nicolas Sarkozy's government from 2007 to 2011.
The payout is based on a 1993 case where Tapie sued the French government for compensation after selling his stake in Adidas to the now defunct state-owned bank, Credit Lyonnais. Tapie claimed the bank encouraged him to sell his share in the sportswear company for less than it was worth.
The state initially fought Tapie's claim but changed tack shortly after Sarkozy was elected president. It is alleged that Lagarde's payout was a reward for Tapie backing Sarkozy's election campaign.
The prosecution accused Lagarde of misusing public funds and said the settlement "deprived the state of a chance to avoid this money being misused."
What is Lagarde's response?
Lagarde denied the charges and argued that the payments were made "in the state's interest."
She said the allegations were politically motivated and told the International Monetary Fund (IMF), of whom she is head, that she expects to be cleared of the charges.
Who is Bernard Tapie?
A business magnate turned politician, Bernard Tapie served as Minister of City Affairs for three months under former French president Francois Mitterrand from December 1992.
The 73-year-old is a close friend of Sarkozy and substantially funded his 2007 presidential campaign. He owned the sportswear giant Adidas between 1990 and 1993 but lost control of the company when he went bankrupt. Tapie also owned Marseille Football Club, a top French outfit. The club won the 1993 European Cup and was later involved in a match-fixing scandal.
Investigators in this case allege that the out-of-court settlement benefited Tapie. He was ordered to repay the money last year but he lodged an appeal.
How does this affect the International Monetary Fund (IMF)?
Despite the charges, Lagarde was reappointed in February as managing director of the IMF. The IMF has backed their chief.
But if Lagarde is convicted, the IMF risks damaging its reputation and could plunge the institution into a leadership crisis. Lagarde's predessor, Dominique Strauss-Kahn, resigned in 2011 to fight sexual assault charges.
If convicted, Lagarde could face one year in prison and a fine of up to 15,000 euro.