Former Colonel Laurent Serubuga was taken into custody in northern France in July, two months after a Rwandan court issued an international warrant for his arrest.
Kigali suspects him of involvement in the 1994 genocide, when he was Deputy Chief of Staff in the Rwandan army.
A French court refused last Thursday to approve Rwanda's extradition request, and ordered Serubuga to be released from custody.
The court also rejected the murder charges against the former colonel, on the grounds that the warrent was issued more than ten years after the alleged crimes.
France's Public Prosecutor says it will pursue the case in an exceptional Cassation Court, arguing that the severity of the charges means the extradition deserves special consideration.
Serubuga is thought to have come to France in 1998, and is one of about 20 genocide-related suspects residing in the country.
French courts have repeatedly refused to extradite them to Rwanda, fearing they would not receive fair trials.