* Betancourt reunited with 'babies' who kept her alive

* Bloodless rescue further weakens FARC rebels

* Colombian peso, stocks rise on rescue news

* Betancourt heads to Paris

By Hugh Bronstein

BOGOTA, July 3 (Reuters) - Ingrid Betancourt, the symbol of rebel hostages in Colombia, hugged and wept with her children for the first time in six years on Thursday after a military rescue that dealt a severe blow to already weakened guerrillas.

The rescue was a coup for U.S. ally President Alvaro Uribe and raised the possibility that Latin America's oldest left-wing insurgency is in collapse after it was duped into handing its top bargaining chip to the military in the jungle.

Betancourt, a French-Colombian citizen kidnapped during her 2002 presidential campaign, threw her arms around her two adult children, their eyes tearful a day after her captors unwittingly freed her, three Americans and 11 Colombians.

"What I'm feeling now is something very close to paradise," Betancourt told reporters at an airport in Bogota.

"These are my babies, my pride, my reason for living, my light, my moon, my stars," she said. "Forgive me for saying it, but I think they are very good looking."

Her son and daughter, Lorenzo, 19, and Melanie, 22, flew from Paris with French Foreign Minister Bernard Kouchner as soon as they got news of their mother's rescue from the Revolutionary Armed Forces of Colombia, or FARC.

Betancourt, 46, could not wait for them to exit the plane. She bolted up the steps to smother them in kisses inside.

She said her captivity in secret camps had driven her to think of suicide. She was punished for several escape attempts, chained at the neck to a tree or made to walk barefoot.

Despite looking gaunt and depressed in photographs taken during her captivity, Betancourt appeared in sound health.

The bloodless rescue operation increased public confidence in the iron-willed Uribe, whose father was killed in a botched FARC kidnapping two decades ago.

He is hugely popular for his anti-rebel offensive and his growth-oriented economic policies. The rescue shored up Uribe's support at a time when many of his followers want to change the constitution to let him run for a third term in 2010.

Stocks and the peso currency surged as investors showed increased political confidence in Colombia.

The rescue followed the death of three FARC leaders this year and a call from the group's top ally, Venezuelan President Hugo Chavez, for them to negotiate for peace.

FARC 'TERMINALLY ILL'

The FARC, considered a terrorist organization by U.S. and European officials, finances its war through cocaine trade and still holds hundreds of others, mainly police and soldiers.

But the outlawed rebel army, once a 17,000-member force able to frequently attack major cities, has been driven back by Uribe into remote areas and now has about 9,000 combatants.

"The FARC is terminally ill and every day it is closer to disappearing for good," Martha Lucia Ramirez, a congresswoman and former defense minister said.

The United States said it was aware of the rescue plan, but stressed that it was a Colombian operation.

It has given Colombia more than $5.5 billion in mostly military aid since 2000. U.S. troops in Colombia often help security forces analyze intelligence and plan missions.

The three freed Americans, defense contractors Keith Stansell, Marc Gonsalves and Thomas Howes were flown to the United States after five years in captivity.

In good health, the tall, slim men strode energetically, smiled broadly and slapped the backs of U.S. personnel who helped them leave Colombia.

Late Thursday, Betancourt flew off to France, where she has become a cause celebre and top foreign policy issue due to her nationality through an earlier marriage.

The international attention Betancourt's captivity drew ensured heads of state worldwide welcomed her release.

French President Nicolas Sarkozy will host her in Paris. Next week, the pope is expected to receive the devout Catholic, who made a wooden rosary bead set in the jungle that she used to pray each day and still clutched in her freedom.

Colombia said Wednesday's rescue mission hinged on soldiers posing as members of a fictitious group apparently sympathetic to the rebels. Supposedly they were going to transport the hostages to a FARC commander's camp by helicopter.

Once the aircraft was in the air, the soldiers disarmed two guerrillas and informed the hostages that they were free.

"The only option left for the FARC is to take a more political approach to the Colombian government ... based on the success of Uribe's military policies," said Pablo Casas, an analyst at Bogota think tank Security and Democracy. (Editing by Saul Hudson and Frances Kerry)

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