Yoo Som-Na, 47, was arrested late last month in her Paris residence and detained under an international arrest warrant in connection with possible charges of embezzlement, tax fraud and criminal negligence.
She faces court hearings for an extradition procedure that could take several months.
"We will fight her extradition right to the end and through all means possible and imaginable," her lawyer said on the sidelines of a court hearing in Paris today during which her request to be temporarily set free was rejected.
Korean prosecutors also wish to speak to another son who lives in the United States on related charges.
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Yoo Som-Na's court appearance came as some 6,000 Korean police forced their way into the compound of a religious group in Anseong, south of Seoul, to look for her father.
The huge operation came a day after South Korean President Park Geun-Hye urged police and prosecutors to step up the manhunt for the 72-year-old patriarch of the family behind the Chonghaejin Marine Co.
Seoul has offered USD 500,000 reward for information leading to the arrest of the father and USD 100,000 for Yoo Dae-Kyun.
The 72-year-old has no direct stake in Chonghaejin, but his children and close aides control it through a complex web of holding companies.