Speaking to France's BFM-TV on Thursday, Betancourt's ex-husband, Fabrice Delloye, said: "The first objective of this mission is to succeed in getting close to Ingrid and care for her.
"Then we hope the emissaries will be able to speak with the Farc and consider pulling Ingrid out of the jungle."
|Lorenzo Delloye-Betancourt said his mother|
was dying [AFP]
Pascale Andreani, a French foreign ministry spokeswoman, declined to provide details about the mission at a news briefing on Thursday.
She said: "Discretion is required in this type of case.''
The office of Nicolas Sarkozy, France's president, had said on Wednesday that a joint mission by France, Switzerland and Spain aimed at giving medical aid to Betancourt was on its way to Colombia.
There is no indication as to whether the Farc rebels have given the operation their blessing.
However, Luis Carlos Restrepo, Colombia's peace commissioner, said the Colombian government was complying with a request by France that it suspend all military operations against the Farc while the operation took place.
Speaking at a news conference in Paris on Wednesday, Lorenzo Delloye-Betancourt, Betancourt's son, said these were the final hours of his mother's life unless critical measures were executed immediately
He said: "At the hour that I'm addressing you, in the Colombian jungle, a woman, my mother, is dying. She has Hepatitis B and leishmaniasis which requires a blood transfusion in the hours to come or risks losing her life."
Any successful mission to treat the captives would be the first contact for years with some of the hostages, whom the Farc rebels say they want to exchange for their jailed fighters.
Attempts to secure a deal to free the hostages, who also include three Americans, are deadlocked over a rebel demand that Uribe demilitarise an area in the south of Colombia for a safe haven to facilitate talks.
The Farc did release six captives earlier this year in a deal brokered by Hugo Chavez, Venezuela's president.