Baye was born in Mainneville, Eure, Normandy, to Claude Baye and Denise Coustet, two Painters. At 14 she joined a school of dance in Monaco. Three years later she went to the United States. On returning to France she continued with dance but also registered for the Simon Course and was admitted to the Conservatoire, from where she graduated in 1972 with a second prize in comedy, dramatic comedy and foreign theatre.