Al Jazeera's Mariana Sanchez in Caracas said that the move suggested that the French government was speaking directly to Farc.
"The option at the moment is to think that Ingrid Betancourt is critically ill and they are bowing to requests by the French government to release her," she said.
In an interview to Colombian television earlier this month, Nicolas Sarkozy, the French president, appealed directly to Manuel Marulanda, the Farc leader, for Betancourt's release.
"It's up to him to decide how he wants to appear to the entire world: look like an assassin or like someone who has had the courage to make a humanitarian gesture," he said.
However, Al Jazeera's Mariana Sanchez said that Farc had never before seemed too concerned about hostages dying in captivity, whether they had died of natural causes, been killed by the group or in exchanges of fire with the army.
Betancourt, who was abducted in 2002, is reportedly suffering from hepatitis B and leishmania, a skin disease caused by insect bites.
Fabrice Delloye, her former husband, has expressed doubts about the Colombian government's recent offer to release Farc prisoners, adding that he feared that Betancourt 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 have and are in the process of shielding themselves," he said.
Colombia's government signed a decree after an emergency meeting on Thursday, that would set free Farc rebels if the group first released some hostages, including Betancourt, according to the country's senior peace negotiator.
Francois Fillon, the French prime minister, said on Sunday that Paris was ready to accept Farc rebels released by Colombia.
"France is ready to do whatever is necessary to allow the liberation of Ingrid Betancourt and the reception of Farc activists who are part of this effort," he told TF1 television.
On Saturday, Alvaro Uribe, Colombia's president, said what the Colombian government has found out about Betancourt is "what the whole community has heard - a delicate state".