Stutzmann's musical education included not only singing, but also piano and bassoon studies; she is an accomplished chamber musician on both instruments. After vocal studies at the Ecole Nationale in Paris, she won the 1983 Brussels vocal competition, and made her concert debut in 1985, singing Bach's Magnificat in Paris. In 1986 she performed and recorded Magnard's opera Guercoeur and received positive reviews for performances of Purcell's Dido and Aeneas at the Opéra de Paris. A 1989 recording of Handel's Amadigi (with Marc Minkowski) cemented her reputation, and since that time she has enjoyed an unbroken schedule of performances and recordings. Other notable operatic roles include Gluck's Orfeo, Handel's Giulio Cesare, and Geneviève in Debussy's Pelléas et Mélisande. Her oratorio repertory includes all the major works of Bach, Handel, and Vivaldi. Her discography includes over 60 titles, primarily for RCA Victor, but also for Erato, EMI, Philips, Harmonia Mundi, and Sony. Her volumes of Schumann lieder, and mélodies by Chausson, Fauré, and Poulenc are representative of her best recital work.
In 2009, Stutzmann added another dimension to her artistic pursuits, founding her own chamber orchestra, Orfeo 55. She had studied conducting with Jorma Panula, and the orchestra allows her to apply the same interpretive approach that she used in vocal roles to that of a conductor.