Orange CEO Stephane Richard was held for questioning on Monday over his role in a 2008 arbitration process that resulted in a large pay-out to businessman Bernard Tapie, a judicial source said.
Richard was at the time head of cabinet to Christine Lagarde, who was finance minister to conservative former president Nicolas Sarkozy before she became head of the International Monetary Fund.
Richard has denied any wrongdoing in earlier statements. On Monday a spokesman for him said the questioning could last up to 48 hours before a decision was made on placing Richard under official investigation.
Orange, which has recently changed its name from France Telecom, declined to comment. Its shares traded down 1.09 percent at 7.547 euros at 0847 GMT.
The corruption probe has put Richard, whose contract at the state-backed company is up for renewal next year, in a delicate position with the government, which owns 27 percent of the group and chooses its chief executive.
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The Socialist government has not yet replaced any of the bosses of the major state-owned companies.
"The state in its role as a shareholder will take a position if needed at the right time on the continuing case," Industry Minister Arnaud Montebourg said in a statement.
Authorities are investigating the French government's decision in 2008 to award tycoon Bernard Tapie 285 million euros ($373 million) in damages as part of his long-running battle with now-defunct bank Credit Lyonnais over the 1993 sale of his stake in sports clothing firm Adidas.