Turcotte was found not criminally responsible for the deaths of Anne-Sophie, 3, and Olivier, 5, by an 11-member jury in July 2011. The jury concluded he was mentally ill at the time of the murders.
Turcotte has been held at Montreal's Pinel Institute since that verdict, and officials there have confirmed the former cardiologist has been allowed out for unsupervised bicycle trips as part of his treatment.
In an exclusive interview with CBC, Turcotte's ex-wife and the mother of the slain children, Isabelle Gaston, said she still fears Turcotte will seek her out.
"People say, 'Don't worry, never with this verdict will he try to hurt you,'" Gaston said. "But he was a cardiologist. He had two children, and he still tried to do that."
Prosecutors appealed Turcotte's verdict in September, and they are seeking a new trial based on their belief that Superior Court Justice Marc David erred in offering the jury the option of finding the admitted killer not criminally responsible because of his mental state.
Turcotte's lawyers now have until late November to respond. Meanwhile, a new hearing to review the conditions for Turcotte's release from the Pinel Institute is scheduled for December.