Betancourt said she had "dreamed of this moment for seven years" and praised the "extraordinary Colombian heroes" who had rescued her.
She also thanked Sarkozy for his efforts in securing her freedom.
The French president, who was visibly moved, said: "Ingrid Betancourt, welcome. France loves you."
Barnaby Phillips, Al Jazeera's correspondent in Paris, said: "It's almost surreal, the journey that Betancourt has taken over the last 48 hours, literally from the most austere circumstances possible, in the remote jungles of Columbia.
"I think France plays an important role in her life, she was educated here, her first husband was French, her children are here.
"Also she has realised how ordinary French people have campaigned for her release. She spoke of how she listened whenever she could to French international radio, just how importance those messages were to her.
"I think she was reminded that French people were battling for her release.
On Thursday she had an emotional reunion with her children, sister and former husband, who had had flown to Bogota from France alongside Bernard Kouchner, the French foreign minister.
"Nirvana, paradise - that must be very similar to what I feel at this moment," Betancourt said at a news conference with her family after their meeting.
At a news conference in the Colombian capital she said she had contemplated suicide during her captivity.
But she said that she could not face "what her children would think" if she ended her life.
She also said that, if given the chance, she would have killed one of her captors to escape.
Betancourt was among 15 captives rescued from the Farc in an operation in which the Colombian military tricked the rebels into handing them over.
'A better way'
Betancourt said that the Farc was "finished" as an organisation in its decades-long struggle against the Colombian government and "had to find a different path".
|Two Farc men holding Betancourt
have been arrested [AFP]
"In the midst of destruction comes the opportunity to find direction and a better way," she told journalists.
"As such I hope the Farc understand this is the time to release all hostages."
The group is thought to hold about 30 foreign captives and hundreds more Colombian civilians and security forces members.
On Thursday, Colombian television showed images of two Farc rebels who had been captured in the rescue operation.
The two men, whom authorities said were known by their aliases "Cesar" and "Gafas", appeared nervous and one had a facial wound.