She was finance minister in President Nicolas Sarkozy’s government at the time of the compensation award to Bernard Tapie for the sale of a firm.
Mr Tapie supported Mr Sarkozy in the 2007 presidential election.
Ms Lagarde’s lawyer described the court’s decision as “incomprehensible”, and said the IMF boss would appeal.
In a statement she said she had “always acted in this affair in the interest of the state and in respect of the law”, according to AP.
Mr Tapie was once a majority shareholder in sports goods company Adidas but sold it in 1993 in order to become a cabinet minister in Francois Mitterrand’s Socialist government.
He sued the Credit Lyonnais bank over its handling of the sale, alleging that the partly state-owned bank had defrauded him by deliberately undervaluing the company.
His case was later referred by Ms Lagarde to a three-member arbitration panel which awarded the compensation, causing a public outcry.
Investigators suspect he was granted a deal in return for his support of Mr Sarkozy.
Earlier this month, a French court ruled that Mr Tapie was not entitled to any compensation for that sale and should pay back the €404m with interest.
France’s Court of Justice of the Republic (CJR) decided that Ms Lagarde, 59, should be tried on the charge of “negligence by a person in position of public authority” over the compensation case, iTele TV channel and the Mediapart website reported on Thursday.
A court spokesman later confirmed the decision.
French media said the CJR investigation magistrates declined to follow the recommendation of another court which last year decided not to pursue the case.
“It’s incomprehensible,” Ms Lagarde’s lawyer Yves Repiquet told iTele. “I will recommend Mrs Lagarde appeal against this decision.”
A spokesman for France’s attorney general said Ms Lagarde would have five days to appeal, once the court decision is made public on Friday or Monday.
Meanwhile, IMF spokesman Gerry Rice said the organisation – which represents 188 member nations – “continues to express its confidence in the managing director’s ability to effectively carry out her duties”.
Ms Lagarde replaced Dominique Strauss-Kahn as IMF managing director in 2011.
Mr Strauss-Kahn – also a former French minister – resigned following his arrest in New York on charges of sexual assault that were later dropped.