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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.
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.
If convicted, she could be sentenced to one year in prison.