Born in 1962 in Orthez, Suhubiette played the piano very early. He then went on to undertake musical studies at the. He joined the early music department where he studied singing with John Elwes and Guillemette Laurens. At the University of Toulouse Le Mirail he studied musicology and choral conducting with Alix Bourbon, whose vocal ensemble he joined which allowed him, at a very young age, to sing under the direction of Michel Corboz, Jean-Claude Malgoire, Gustav Leonhardt etc. It was at this time, in 1985, that he founded Les Éléments with friends singers from the Conservatoire and the University, an ensemble that later became the chamber choir he still conducts in Toulouse. He then began his professional career as a singer with Les Arts Florissants of William Christie. In 1986 his meeting with Philippe Herreweghe played a decisive role: for twelve years he sang in his ensembles – La Chapelle Royale and the Collegium Vocale Gent – with which he took part in more than thirty recordings and discovered the diversity of the vocal repertoire to which the Belgian conductor devoted himself with his two prestigious choirs. Soon, Philippe Herreweghe made him his assistant and he was entrusted with the preparation of the choir for productions and recordings. In 1993, Suhubiette took over the management of the Ensemble Jacques Moderne, whose founder Jean-Pierre Ouvrard died at the end of 1992. It was the beginning of a new musical adventure that immersed him in the universe of a cappellapolyphony of the French, English and Spanish Renaissance music to which he dedicated some of his recordings.. Very soon, he extended the ensemble's repertoire to the composers of the 17th and 18th centuries, giving a preponderant place to the works of the first German Baroque,. A little later, he performed with l'Ensemble the motets, passions, Mass in B minor and short masses by Johann Sebastian Bach, anthems by Purcell and Handel, Purcell's operas , and the French Baroque repertoire. As early as 1997, with the chamber choir Les Éléments he conducted in Toulouse, he began conducting the a cappella repertoire of the 19th and 20th centuries, the Baroque oratorios classical and commissioned a large number of works from contemporary composers. He also plays Stravinsky, Poulenc, Britten, Dallapiccola, Berio, Mantovani, Dusapin. Thanks to his assiduous practice of the a cappella repertoire, the chamber choir "Les Éléments" was one of the most important choirs in France, and with it, Suhubiette performed in Europe, the USA, Canada, Tunisia, Lebanon, Egypt. The ensemble was the guest of many conductors, the comedy operas by Jacques Offenbach, the French premiere of Kurt Weill's Der Silbersee at the Massy Opera House, Les caprices de Marianne'' by Henri Sauguet. In the oratorio domain, the programmes led him to conduct the Orchestre national du Capitole de Toulouse, the Orchestre de Chambre de Toulouse, the Orchestre Baroque Les Passions, Les Folies françoises, the Café Zimmermann, Gli Incogniti, Concerto Soave, the Ensemble Baroque de Limoges, the Pau-Pays de Béarn orchestra, Les Percussions de Strasbourg, Ensemble Ars Nova etc. It is in this spirit of openness to several musical worlds that the Abbey-school of Sorèze in the Tarn département offered him in 2006 to become artistic director of its festival. Since 2008, Suhubiette has been teaching regularly in the choir conducting class of the Conservatoire national supérieur de musique et de danse de Lyon. In 2014, he was awarded the rank of Officer of the Order of Arts and Letters by the French Ministry of Culture.