NEW YORK — Leslie Caron carries a souvenir of making the classic 1951 film "An American in Paris" with her every day.The 84-year-old French beauty wears a ring she bought with her first paycheck from the Gene Kelly film. Back then, she was a shy teenage ballerina and the jewelry she picked made a statement: A phoenix with a globe in its talons."It means I can grapple the world," the actress said late last week in the midst of a whirlwind trip to New York.Two people who gazed reverentially at her ring in her hotel suite were two young dancers who know exactly how she must have felt — Robert Fairchild and Leanne Cope, currently starring in the lush Broadway musical "An American in Paris."Like Caron, Fairchild and Cope are ballet dancers who spread their wings into another medium thanks to the power of the story set in post-war Paris with Gershwin songs."That's what changed your life," said Fairchild, a principal dancer with the New York City Ballet, speaking to Caron.