"I believe ... that the outcome will be happy and will end soon, in this sad case of the freeing of hostages," he said.
Ahead of his visit to Venezuela, Kouchner had also held talks in Colombia and Ecuador with their leaders, Alvaro Uribe and Rafael Correa.
France sent a medical mission to Colombia following reports from former hostages that Betancourt, who has been held for six years, was suffering from hepatitis B, depression and a skin disease and was close to death.
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 Farc wants a large demilitarised zone to be created in the country for negotiations over the hostages to take place, however the Colombian government wants a smaller area to be used.