The chief executive of the telecoms firm, France Telecom-Orange, has been held in custody for questioning in a corruption case.
Stephane Richard, who previously worked in the French Finance Ministry, was quizzed over his role in a 2008 payment made to the businessman Bernard Tapie.
Mr Richard denies any wrongdoing.
Christine Lagarde, the head of the International Monetary Fund, has also been called upon to testify in the case.
Ms Lagarde was the French Finance Minister at the time in question while Mr Richard was her chief of staff.
France Telecom-Orange said the questioning was expected and that Mr Richard remained in charge. He can be held for up to 48 hours.
His contract at the partly state-owned company is up for renewal next year and the position is chosen by the government.
"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.
The Court of Justice of the Republic, which investigates ministerial misconduct in France, is looking into claims that Mr Tapie may have received favourable treatment because of his support for the former President, Nicolas Sarkozy.
He received a payment of 400m euros ($520m; £340m) as part of a settlement in a long-running business dispute, which critics say was too generous.
After two days of questioning Ms Lagarde was made a key witness in the case - a status that means she is unlikely to be prosecuted.