Venezuelan President Hugo Chavez and French President Nicolas Sarkozy met in Paris on Tuesday (November 20) to discuss the fate of a high-profile French hostage held by Colombian rebels who Chavez believes is still alive. Sarkozy has made securing the release of French-Colombian politician Ingrid Betancourt one of his foreign policy priorities and Chavez, who pointed out his mediating effort has paid off so far, hopes to negotiate a prisoner exchange with the rebels holding her. Chavez has been mediating efforts between Colombia's government and the Revolutionary Armed Forces of Colombia (FARC), a guerrilla group that has waged a four-decade war against the state. "Ingrid is alive I am completely certain," Chavez said. Chavez said he and Sarkozy were "very optimistic about the possibility of liberating not only Ingrid but all the people who are being held hostage by the FARC." "In three months, we have made more progress than what has been accomplished in the last five years," Chavez said. Sarkozy and Chavez also met relatives of Betancourt, a former Colombian presidential candidate who was kidnapped along with her campaign aide Clara Rojas in February, 2002. Betancourt's mother and daughter have led an emotional campaign for Ingrid's release for years. Yolanda Pulecio, Ingrid's mother, said: "President Chavez is certain that Ingrid is alive - that proof should come. It was not easy to do but they will manage to do it," Melanie Betancourt, Ingrid's daughter, said: "President Chavez assured us that my mother is alive. He's sure of that, but now we still need proof of life because it's an essential element for things to advance in the negotiations. It will prove the desire and seriousness of the FARC to proceed in this case," Chavez has repeatedly said he hopes to bring to light proof that Betancourt is alive, but so far there has been no indication that he as obtained such proof. On Tuesday he said the rebels had promised proof by year's end. The Marxist FARC wants rebels held in government prisons to be freed in exchange for its most high-profile captives, including Betancourt and three U.S. contract workers held for years in jungle camps. Neither Betancourt nor Rojas have been heard from since 2003.