He sang at the Théâtre du Châtelet, during the 1951–52 season, as a double for Luis Mariano in the operetta Le Chanteur de Mexico, while taking voice lessons with Rolande Darcoeur in Paris.
Vanzo was then immediately invited to sing at the Opéra-Comique and at the Palais Garnier, quickly establishing himself in the standard French lyric repertory in roles such as Nadir in Les pêcheurs de perles, Gérald in Lakmé, Faust, Roméo in Roméo et Juliette, Vincent in Mireille, des Grieux in Manon, etc.
He won great acclaim at the Palais Garnier in 1960, as Edgardo in Lucia di Lammermoor, opposite Joan Sutherland who was making her debut there.
He sang at Carnegie Hall in New York, as Gennaro, in the famous 1965 concert version of Lucrezia Borgia, opposite Montserrat Caballé.
As the years went by, Vanzo extended his repertory to more dramatic roles, such as Arrigo in the original French version of I Vespri Siciliani, Adorno in Simon Boccanegra, Cavaradossi in Tosca, Robert in Robert le Diable, Raoul in Les Huguenots, Mylio in Le roi d'Ys, and became internationally renowned as one of the best exponents of the role of Benvenuto Cellini and Werther.