A French court has ordered that Christine Lagarde, the International Monetary Fund chief, be investigated for the role that she played in a financial settlement paid to a friend of President Nicolas Sarkozy during her tenure as finance minister.

Lagarde is accused of misconduct for overruling objections from advisers to approve a $407m arbitration payout to Bernard Tapie in 2008. Tapie had a long-running legal dispute with Credit Lyonnais, a former state-owned bank.

He claimed that the bank defrauded him when it sold his stake in Adidas sports clothing group in 1993.

Critics argue that the legal battle should not have gone to private arbitration, as it involved a state-owned bank.

Thursday's order came as no surprise to Lagarde.

Her lawyer, Yves Repiquet, said that Lagarde had been relieved to hear the news - as it ended months of speculation over whether a complaint submitted by opposition groups would result in a probe.

In an emailed statement, Repiquet said: "This procedure is in no way incompatible with the current functions of the managing director of the IMF."

Lagarde was appointed head of the IMF last month after her predecessor, Dominique Strauss-Kahn, was charged with sexually assaulting a New York hotel maid and quit.