Born in Lyon, Soustrot first studied there at the Conservatoire de Lyon from 1962 to 1969. He continued his studies at the Conservatoire de Paris, in particular in piano, trombone, chamber music, and conducting. In 1974 he won first prize in the international conducting competition in London, which led to becoming assistant conductor to André Previn at the London Symphony Orchestra, and in the following year succeeded Jean-Claude Casadesus as assistant conductor of the Orchestre national des Pays de la Loire of which he became music director from 1976 to 1994. Soustrot resigned as director of the Opéra de Nantes in 1989 in protest at a 50% reduction in its state subsidy following a change of government in Nantes after local elections, also accusing the French government of diverting money from provincial companies to the Opéra Bastille. From 1995 to 2003, he was GMD of the Beethoven Orchester Bonn, where he conducted the first performance of Beethoven's Leonore, the first version of the later Fidelio, since 1806. He led the Brabants Orkest Eindhoven from 1996 to 2006. From the 2011/12 season, he has been the Malmö Symphony Orchestra's Chief Conductor, and from the 2015/16 season also conductor of the Aarhus Symphony Orchestra. He conducted at the Staatsoper Stuttgart Gounod's Faust, Bizet's Carmen, and Wagner's Siegfried and Götterdämmerung. He conducted Debussy's Pelléas et Mélisande at the Semperoper in Dresden, staged by Àlex Ollé of the company La Fura dels Baus. In a run of Offenbach's Les Contes d'Hoffmann in Geneva, one critic wrote "The Orchestre de la Suisse Romande sparkled under Marc Soustrot, Soustrot's light touch and dramatic punch gave the evening an atmosphere of momentum and musical brilliance, and helped one to forget the stylistic imbalances in the music. For his conducting of Berg's Wozzeck, he was described as "an impressive conductor, avoiding anything artificial but aiming for what Berg had in mind: a sensual effect of magnificent sounds." He conducted in 2017 at the Oper Frankfurt a double bill of Debussy's cantata La Damoiselle élue and Honegger's dramatic oratorio Jeanne d'Arc au bûcher, again staged by Ollé, and co-produced with the Teatro Real Madrid. A reviewer noted that the conductor "creates a unique musical wonderworld", with pianos, celesta and Ondes Martenots highlighting special moments. Hans-Klaus Jungheinrich wrote in the Frankfurter Rundschau: "Umsichtig und stilgenau differenzierten Gastdirigent Marc Soustrot und das Opernorchester zwischen der behutsam abgetönten Debussy-Klanglichkeit und dem breiten Pinsel einer auch gröbste Wirkung souverän einbeziehenden Interpretation der Honegger-Textur.". He is from a musical family; his younger brother is the trumpet-player Bernard Soustrot.