Betancourt's mother said she was confident that Kouchner's visit would bring some progress in engineering her daughter's release.
"This is a big example of the interest that France continues to have to help us with the liberation of Ingrid and all the hostages," she said.
"I have a lot of expectations because he [Kouchner] is going to talk to President Uribe."
Betancourt, a former Colombian presidential candidate, has been held in captivity for six years.
France sent a medical mission to Colombia this month to try to treat Betancourt after reports from her family and former hostages that she was suffering from hepatitis B, depression and a skin disease, and was possibly near death.
Kouchner, left, with former hostage Clara Rojas,
hopes to secure Betancourt's release [AFP]
However, Revolutionary Armed Forces of Colombia (Farc) rebels refused to receive the mission, saying that it did not respond "to blackmail nor media campaigns", and France called it off.
France has backed proposals to swap Farc rebels for about 40 high profile hostages the group holds, including Betancourt and three US Pentagon contractors.
The rebels say they want Uribe to demilitarise a large area of Colombia in order to hold talks on the hostages.
|Raul Reyes, left, was killed in a Colombian|
cross border raid on March 1 [AFP]
Uribe has argued for a smaller zone, saying a larger one would allow the rebels to regroup.
In January the group, which has been fighting a war against the Colombian government for decades, released six Colombian hostages following negotiations brokered by Chavez.
However negotiations were severely curtailed by a controversial cross-border raid on a Farc rebel camp in Ecuador by Colombian forces on March 1 which left several rebels dead, including senior leader Raul Reyes, with whom France had been negotiating Betancourt's release.