Dieter Krombach, 77, was sentenced last year to 15 years in prison over the death of his 14-year-old step-daughter Kalinka at their German home in 1982.
In a case that captivated France, Kalinka's biological father, André Bamberski, took the law into his own hands after Germany refused to hand Krombach over, employing a team of kidnappers to drag him to France before dumping him near a courthouse.
Krombach's lawyers were set to argue that his trial in France is illegal because of the manner in which he was brought to the country.
They also claim the trial cannot be conducted fairly because it lacks access to evidence in Germany.
"He is being asked to defend himself but there is an Iron Curtain between France and Germany that prevents us from having access to evidence," said Krombach's lawyer, Philippe Ohayon.
A Paris court convicted Krombach of "deliberate violence leading to involuntary death" in October 2011.
Bamberski, a 75-year-old who is also facing charges of kidnapping in the case, said before the appeal that he hope the new trial would lead to an even harsher conviction.
"I expect Mr Krombach to be convicted of . . . murder, aggravated murder against Kalinka who was less than 15 years old," he said.
A ruling in the appeal is expected on December 14th.
Kalinka was found dead in her bed at the home she shared with her younger brother, her mother and Krombach and their two children near Lake Constance in southern Germany in July 1982.
An autopsy proved inconclusive as to the cause of death, but forensic examinations of the body called into doubt Krombach's account of her final hours.
A German investigation into her death found there was not enough evidence to charge Krombach but Bamberski, convinced the German had raped and killed his daughter, brought charges against him in France.
A French court in 1995 found him guilty in absentia, but Germany refused to send Krombach to France and the conviction was eventually overturned.
Krombach's credibility was weakened in 1997 when the cardiologist was convicted of drugging and raping a 16-year-old patient, handed a suspended sentence and had his licence suspended.
In October 2009, frustrated by Germany's refusal to send Krombach to France, Bamberski hired a kidnap team who snatched the doctor from his home in Scheidegg, brought him to France and left him, bound and gagged, near the courts in the border town of Mulhouse.
Krombach was promptly arrested.