Born in Marseille, Crespin studied at the Paris Conservatoire, and debuted at the Paris Opera as Elsa in Wagner's Lohengrin in 1950. After a period of singing with smaller French companies, she made debuts at Bayreuth in 1958, the Glyndebourne Festival and Vienna State Opera in 1959, Covent Garden in 1960, and the Met in 1962.

Her signature roles included the Marschallin in Strauss's Der Rosenkavalier, Kundry in Wagner's Parsifal, the title role in Gluck's Iphig_nie en Tauride, and the title role in Bizet's Carmen. She retired in 1989.