WRAPUP 6-Ex-hostage reunited with children in Colombia

* 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.