"I thank God for this moment. These are my little ones, my pride, my reason for living, my light, my moon, my stars. For them I wanted to leave the jungle, to see them again," she said.
The office of Nicolas Sarkozy, the French president, said Betancourt herself would travel to Paris from Colombia later on Thursday.
Al Jazeera's Nick Clark in Paris says the city has been gripped by the fate of Betancourt and her cause was widely supported by the French people.
Betancourt had said earlier she was probably alive today thanks to France's efforts on her behalf.
"I want to tell President Sarkozy - and through him all the French people
- that they were our support, our light,'' she told RCN, a Colombian television station.
Meanwhile Hugo Chavez, the Venezuelan president who had previously helped secure the release of several Farc hostages, said on Thursday that he was "overjoyed" at the "liberation" of the captives.
Friends and family of Betancourt, who was seized while campaigning for the Colombian presidency in 2002, had campaigned for years to secure her freedom.
Betancourt's health had reportedly been failing in recent months and her family had said she was severely depressed, close to death and in urgent need of medical treatment.
One of her first acts after regaining her freedom was to visit the grave of her father in Colombia, who died while she remained in captivity.
"God, this is a miracle, such a perfect operation is unprecedented"
rescued Farc hostage
Betancourt had been held by the Farc in remote jungle territory near the city of San Jose del Guaviare.
She and the others were flown from the region to the Catam military base for medical treatment following the operation to free them.
At a news conference, Betancourt described her years in captivity and the operation to release her, praising the Colombian and French leaders as well as the Colombian army, often crying as she spoke.
"God, this is a miracle, such a perfect operation is unprecedented," she said.
Three US hostages, former defence contractors, also freed during the operation, were flown back to a US military base in San Antonio, Texas, after their release.
At a press conference on Thursday, US military officials said the men were in good health.
'You are free'
Juan Manuel Santos, the Colombian defence minister, said the operation began when the military spies infiltrated the Farc and tricked the rebel commander holding the hostages into thinking the hostages were to be taken to Alfonso Cano, the group's top leader.
|The three US Pentagon contractors were
seized in 2003 [EPA]
Betancourt later said at the press conference following her release that the hostages, who had been divided into three groups, were taken to a rallying point on Wednesday morning where two disguised helicopters piloted by Colombian military agents were waiting.
It was not until the helicopters were airborne, Betancourt said, that the mission's commander turned to her and said: "We are the national army, you are free."
Santos also said that two rebels on the aircraft were detained but that no Farc rebels on the ground were hurt during the operation and they were permitted to escape "in hopes that they will free the rest of the hostages".
Al Jazeera's correspondent Mariana Sanchez in Bogota says other details have emerged indicating the operation had been planned by the Colombian military for some time.
Much information on the hostages' location and condition coming from a Colombian policeman who had been held alongside Betancourt and the US contractors, and who escaped after almost a decade in captivity.
Colombian military authorities also managed to intercept a video tape featuring Betancourt from two female Farc members who were seized, our correspondent says.
Farc in decline
The Revolutionary Armed Forces of Colombia [Farc] has been fighting the Colombian government for more than 40 years
It thought to have been weakened by desertions and the killing of two of its senior leaders, and in May it said that its top commander, Manuel Marulanda, had died of a heart attack.
Analysts say the operation's success strengthens Colombian president Alvaro Uribe's already high popularity and puts further pressure on the Farc, which has already been weakened by the loss of key leaders and desertions.
The Farc is thought to be holding a total of about 700 hostages, including around 40 from outside Colombia and the group had said it may exchange them in return for the release of it fighters captured by the government.
Al Jazeera's Rosalind Jordan said there were concerns over what the Farc might do with those still in captivity following the loss of Betancourt, who had been their most high-profile hostage.