Connesson studied the piano, music theory, music history and choir conducting at the Conservatoire National de Région de Boulogne-Billancourt and composition with Marcel Landowski for six years from 1989. In the Conservatoire National de Région de Paris, he studied orchestral conducting with Dominique Rouits and orchestration with Alain Louvier.

As a composer, he asserts influences as various as François Couperin, Richard Wagner, Richard Strauss, Claude Debussy, Maurice Ravel, Igor Stravinsky, Olivier Messiaen for the Turangalîla-Symphonie and Saint François d'Assise, Henri Dutilleux for his Métaboles, Steve Reich, and also John Adams but also movie composers such as Bernard Herrmann or John Williams or the funk style of James Brown.

From 2001 to 2003, he was composer in residence at the Orchestre National des Pays de la Loire, for which he wrote the vocal symphony Liturgies de l'ombre and the symphonic poem L'appel au feu. He is currently composer in association with the Royal Scottish National Orchestra; his music is played by American and English orchestras such as the Cincinnati Symphony Orchestra, the Philadelphia Orchestra, the Houston Symphony Orchestra, the Saint Louis Symphony Orchestra, and the BBC Symphony Orchestra. From 2009 he has been composer in residence at the Orchestre de Pau, Pays de Béarn.

Instrumentation: Clarinett and Cello.