"We do not have any information about an imminent release but we don't want to leave any stone unturned on our side," a source in the French presidency told the Journal du Dimanche.
The plane is parked at a military base in Cayenne, the source said.
The report comes after Betancourt's former husband Fabrice Delloye told AFP that he feared she was "either dying or already dead."
"What worries me most is the latest statement by the Colombian government, and I wonder if they have information that we do not and are in the process of shielding themselves."
Betancourt, a senator who is being held by guerrillas from the Revolutionary Armed Forces of Columbia (FARC), is reportedly very ill.
Colombia's independent public ombudsman, Volmar Perez, earlier said reports indicated that "the state of her health is very delicate, and her physical and health conditions have been deteriorating".
He said that, according to residents in an area where Betancourt was taken by her captors to be treated, the high-profile hostage was suffering from hepatitis B and leishmania, a skin disease caused by insect bites.
Betancourt is among 39 high-profile hostages, including three US defence contractors, whom the FARC wants to exchange for 500 rebels held in prison.
Direct talks to negotiate the prisoner swap have never begun, although the rebels unilaterally released six hostages to Venezuelan President Hugo Chavez earlier this year. (AFP)
France ready to retrieve hostage amid health fears