Judicial sources said a judge had decided against releasing Yoo Som-Na, 47, on bail following her arrest on yesterday under an international arrest warrant.
Korean authorities want to talk to her in connection with their investigation into a sinking that claimed around 300 lives, most of them schoolchildren.
A decision on whether Yoo should be extradited is likely to take months as French authorities will have to satisfy themselves that there is a legitimate basis for the request.
Yoo Som-Na is the daughter of Yoo Byung-Eun, the head of the family which controls Chonghaejin Marine Co., the company which owned and operated the Sewol ferry that capsized and sunk on April 16 with hundreds of high-school students on board.
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Yoo and his eldest son Yoo Dae-Kyun are being hunted by Korean authorities who suspect breaches of legal safety standards may have led to a tragedy that moved the whole world.
Korean prosecutors want to question the two men, Yoo Som-Na and another son who lives in the United States in connection with possible charges of embezzlement, tax fraud and criminal negligence.
Yoo has no direct stake in Chonghaejin, but his children and close aides control it through a complex web of holding companies.