The Colombian military has released a video recorded during the rescue of 15 rebel hostages that shows them sobbing with joy after they realized they had been freed.

The video was released Friday in Bogota to answer questions about the rescue operation.

Defense Minister Juan Manuel Santos denied reports that millions of dollars in ransom had been paid for the hostages' release.

Also Friday, French-Colombian politician Ingrid Betancourt was welcomed in Paris by French President Nicolas Sarkozy and his wife Carla Bruni. Betancourt was rescued after six years in captivity.

Betancourt told well-wishers she had been dreaming of her homecoming for years, and she tearfully thanked France for campaigning for her release.

She also thanked the Colombian government for executing what she called a "flawless" non-violent rescue.

Betancourt said she was sustained by her Catholic faith, and she called her rescue a miracle from the Virgin Mary. Pope Benedict has invited her to the Vatican for a meeting.

Betancourt was reunited with her son and daughter in Bogota Thursday, less than one full day after the Colombian military rescued her and 14 others, including three American defense contractors, from the Revolutionary Armed Forces of Colombia (FARC).

Authorities say Colombian intelligence officials tricked rebels into handing over their most prominent hostages for transport by helicopter to another location. The hostages boarded what turned out to be government helicopters that flew them to safety.

The operation is widely described as an embarrassing setback for the FARC, which has lost some of its senior commanders in recent months. Desertions also have trimmed its ranks.

Betancourt was seized in 2002 while campaigning for the Colombian presidency. The three American contractors were kidnapped in 2003 when their small plane crashed in the Colombian jungle during a counter-narcotics operation.

The United States, Colombia and European Union have designated the FARC a terrorist organization. The group is believed to be holding more than 700 hostages in jungle locations.

Some information for this report provided by AP and AFP.