Connesson studied the piano, music theory, music history and choir conducting in Conservatoire National de Région in Boulogne-Billancourt and composition by Marcel Landowski during six years from 1989.
With Dominique Rouits, in Conservatoire National de Région of Paris, he also studied the orchestral conducting and with Alain Louvier, the orchestration.
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 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 associated with Royal Scottish National Orchestra and played by the American and English orchestras such as Cincinnati Symphony Orchestra, Philadelphia Orchestra, Houston Symphony Orchestra and BBC Symphony Orchestra. From 2009, he is composer in residence at Orchestre de Pau, Pays de Béarn.
Connesson teaches orchestration at the Conservatoire National d’Aubervilliers-la Courneuve.