Left-wing rebels from the Revolutionary Armed Forces of Colombia (Farc), were tricked into handing over the hostages.
Ms Betancourt had been kidnapped by the group in 2002 while she was campaigning to be president.
Ms Betancourt, who was born in Colombia but spent much of her early life in France, praised Mr Sarkozy as an "extraordinary man".
She said France's influence had helped the rescue operation pass off peacefully, and thanked the French people for their support saying: "I owe everything to France."
She said: "I have cried a great deal during this time from pain and indignation, today I am crying because of joy."
President Sarkozy was waiting with his wife, Carla Bruni, for Ms Betancourt's arrival at the military airfield near Paris on Friday.
Ms Betancourt and her family then joined the president at his official residence, the Elysee Palace, for an official welcoming ceremony.
Ingrid Betancourt was greeted by President Sarkozy
Later, she joined hundreds of supporters at Paris's City Hall to tear down a huge poster of her that marked her 2,321 days as a hostage.
Ms Betancourt's arrival in Europe came as the Vatican said in a statement that the Pope had sent a telegram to her expressing his happiness at her rescue.
The Pope will also meet her as soon as it can be arranged, the Vatican statement added.
The BBC's Jonny Dymond in Paris says coverage of her liberation and subsequent movements has been pretty much non-stop on French TV and radio.
Ms Betancourt was campaigning for the presidency against current incumbent Alvaro Uribe when she was kidnapped by Farc guerrillas.
After her release she thanked Mr Uribe and said she still aspired "to serve Colombia as president".
Mr Uribe was first elected president in 2002. He has pursued a hardline stance against Colombia's left-wing guerrilla groups while making tentative peace overtures.
CAPTIVITY TIMELINE
Feb, 2002: Betancourt kidnapped by Farc rebels
Feb, 2003: US defence contractors Thomas Howes, Keith Stansell and Marc Gonsalves seized by after their plane goes down in southern Colombia
Jan, 2008: Betancourt aide Clara Rojas and ex-congresswoman Consuelo Gonzalez freed by Farc
March, 2008: Colombian forces raid rebel camp in Ecuador and kill Farc commander Raul Reyes
March, 2008: Farc leader Manuel Marulanda dies of reported heart attack
July, 2008: Colombian military frees Ms Betancourt, the three US contractors and 11 other hostages
The Farc, which has been waging a guerrilla war to establish a Marxist government for the past four decades, still holds as many as 700 hostages.
Wednesday's successful rescue by Colombian security forces was launched after a disgruntled Farc member infiltrated the group's leadership on behalf of the government.
He convinced them to move Ms Betancourt and 14 other hostages to a rendezvous point in the jungle.
Waiting there were Colombian soldiers, posing as members of a non-government organisation.
The local commander in charge of the hostages and another rebel were captured. They now face extradition to the US.
Colombian Vice-President Francisco Santos told the BBC that it was the beginning of the end of the Farc.
He said the government was weakening the rebels to a point of no return.
Ms Betancourt later had a tearful reunion with her two children, Melanie and Lorenzo Delloye-Betancourt, who had flown to the Colombian capital Bogota from France.
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