A bail judge held a hearing at the Hotel-Dieu hospital in Paris and ruled that German cardiologist Dieter Krombach should be held under the warrant issued following his 1995 conviction by a French court.
Due to the injuries he suffered during the kidnapping, Krombach, 74, will remain in hospital.
French prosecutors on Tuesday pressed preliminary charges against the father of the murdered girl, Frenchman Andre Bamberski, 74, for Krombach's kidnapping and beating.
Krombach was found before dawn on Sunday in a doorway in the eastern French city of Mulhouse, just over the German border, bound and gagged and bleeding from a head injury.
A French court in 1995 convicted the doctor in absentia of manslaughter over the death of 14-year-old Kalinka Bamberski, his stepdaughter, who died at his home in Lindau in Germany in 1982 after he gave her a mysterious injection.
Berlin had refused to hand him over to the French courts, who sentenced him to 15 years of jail, on the grounds that he had already been tried and acquitted in Germany.
Bamberski, who had long pressed for Krombach's arrest, told journalists after being released on bail that he had ordered the doctor's kidnapping and delivery to France, but denied ordering him to be beaten.
The German doctor won a 2001 case against France before the European Court of Human Rights, which ruled that he had been denied a fair hearing and the right to an appeal in the case.
A German court convicted the cardiologist in 1997 of sexually abusing a 16-year-old patient after injecting her with anaesthetic in his surgery. He was handed a two-year suspended sentence and stripped of his licence.
In 2007 he was convicted of fraud for continuing to practice illegally.