Lagarde, who always denied wrongdoing, was not present in court, having left France for Washington.
The IMF board is to meet "shortly" to consider the latest developments.
On Friday, Lagarde told the trial she had always acted in good faith.
Verdicts of the Court of Justice of the Republic (CJR) are not subject to appeal, French media say.
Nonetheless, Lagarde`s lawyer said his team would consider appealing, Reuters news agency reports.
Lagarde replaced Dominique Strauss-Kahn as IMF managing director in 2011.
Mr Strauss-Kahn - also a former French finance minister - resigned following his arrest in New York on charges of sexual assault that were later dropped.
Another former IMF head, Rodrigo Rato of Spain, is currently standing trial on charges of misusing funds when he was head of Spanish lender Bankia.
Public outcry
Lagarde, 60, was tried on charges of "negligence by a person in position of public authority".
Accused of allowing the misuse of public funds, rather than actual corruption, she could potentially have been sentenced to a year in prison.
The CJR is composed mostly of politicians rather than judges, and handles allegations of crimes committed by cabinet ministers in office.
The case originates in the early 1990s, when Mr Tapie was a majority shareholder in sports goods company Adidas.
After launching a political career and becoming a cabinet minister in Francois Mitterrand`s Socialist government in 1992, Mr Tapie had to sell the company.
In 1993, he sued Credit Lyonnais, a state-owned bank that handled the sale, alleging that the bank had defrauded him by deliberately undervaluing the firm.
By 2007, the long-running case was referred to binding arbitration by Lagarde, who at that time was finance minister under conservative President Nicolas Sarkozy.
A three-member panel awarded the compensation a year later, causing a public outcry.
Last year, after eight more years of legal wrangling, a French court ruled that Mr Tapie had not been entitled to compensation and should repay the €404m.
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