Stéphane Belmondo was born on 8 July 1967 in Hyères, on the Var coast, into a household where the instrument came before the choice of one. His father Yvan was a professional saxophonist who ran a big band; his elder brother Lionel, a saxophonist, flautist and arranger, has been his closest musical partner for more than forty years. Stéphane started on drums and percussion at six, took up the accordion at eight, and had moved to the trumpet before he turned ten. He entered the classical accordion class at the Aix-en-Provence conservatory at twelve and the cornet class at fourteen, then the trumpet class at the Marseille conservatory at sixteen. At fourteen he was already on the bandstand, playing tango and bal musette accordion in his father's and Lionel's big band. At fifteen the brothers formed the quintet that would carry their name, with Philippe Milanta on piano, Thomas Bramerie on bass and Bruno Ziarelli, later Vincent Séno, on drums.

He took first prize in trumpet at Marseille in 1986 and went straight to Paris at nineteen, where Séno got him hired at the Club Saint-Germain, later Le Bilboquet. The pianist René Urtreger put him on stage repeatedly and in company that would have been implausible for a teenager from the Var a year earlier, including the Danish bassist Niels-Henning Ørsted Pedersen. He worked through the city's older generation of accompanists: Michel Graillier, Alain Jean-Marie, Georges Arvanitas, Maurice Vander, Pierre Michelot, Al Levitt and André Ceccarelli among them. In 1987 he joined Laurent Cugny's Big Band Lumière, the orchestra that had persuaded Gil Evans to come to France and write for it, and played on both records that partnership produced, Rhythm-A-Ning (1988) and Golden Hair (1989), plus the European tour behind them. Evans is the arranger he names as his principal source of inspiration, and the encounter arrived when Belmondo was twenty.

The other formative meeting of that year involves Chet Baker, who was living out his last months in Europe. The account, given on French Wikipedia and repeated in Vincent Bessières's liner notes for a later Belmondo album, is that Baker heard him at the Paris club Le Palace and had him join the following night's set at the New Morning. French Wikipedia flags its version as needing a source, and both surviving tellings run through people close to Belmondo, so it is offered here as the story he and his circle tell rather than as an independently documented fact. What is not in doubt is how the connection settled into the music: three decades later he recorded Love For Chet, and the pianist he chose for two of his own leader dates, Kirk Lightsey, had been one of Baker's late accompanists.

Between 1987 and 1990 Belmondo worked in Kirk Lightsey's quartet and in bassist Pierre Boussaguet's quintet, the latter alongside Lionel and a young Jacky Terrasson. The Boussaguet band produced a record on which Belmondo played next to Tom Harrell, one of the American trumpeters he had grown up listening to. He detoured through the fusion group Abus, led by guitarist Pierrejean Gaucher, which took him as far as Chile in 1990, then joined Michel Legrand's big band, where he was on stage at the Olympia in 1992 for Legrand's first meeting with the violinist Stéphane Grappelli and on the resulting Verve album. From 1989 to 1993 the Belmondo brothers held a standing engagement in the house rhythm section at the Club Saint-Germain, and out of those nights the quintet reformed with Henri Florens on piano, Bramerie on bass and Jean-Pierre Arnaud on drums. It cut Jazz à Reims in 1993 and For All Friends for the Dutch Challenge label in 1994, and the Académie du Jazz gave the brothers its Prix Django Reinhardt as French musicians of the year.

In 1994 the brothers joined Dee Dee Bridgewater's group for Love and Peace, her tribute to Horace Silver, which also features Jimmy Smith on organ. Belmondo followed the tour to the United States, playing Newport and Carnegie Hall, and moved to New York, where he stayed for several years. English and French Wikipedia disagree on the year of the move, giving 1994 and 1995 respectively, and no source settles it. In New York he formed a quartet with James Hurt on piano, Ugonna Okegwo on bass and Nasheet Waits on drums, which worked the Blue Note, and played with Al Foster, Mark Turner, Lew Tabackin and Franck Amsallem. He recorded there with the pianist Donald Brown, a former musical director for Art Blakey, and with Billy Higgins. Back in Paris he taught at the IACP, the professional music school where Lionel ran the teaching programme, worked in André Ceccarelli's and Andy Emler's groups, and in 1999 recorded ameskeri, a flugelhorn-and-guitar duo with Sylvain Luc, at IRCAM's Espace de projection. The duo outlasted almost everything else in his working life.

The 2000s made him a public figure in France rather than a musicians' one. Hymne au Soleil (2003) set twentieth-century French concert composers, Lili Boulanger above all, alongside Fauré, Ravel and Duruflé, reorchestrated by Lionel Belmondo with Laurent Agnès and Christophe Dal Sasso for eleven players drawn from both the jazz scene and the Orchestre National de France; the record is dedicated to Michel Graillier, who had passed away that February. It took three Victoires du Jazz. Wonderland (2004) was the first album Belmondo signed with his name alone, at thirty-six, and it is a programme of Stevie Wonder songs on which he plays trumpet, flugelhorn, French horn, euphonium, ocarina, shell and percussion. Influence (2005) brought in Yusef Lateef, then eighty-four, on tenor saxophone and an armoury of flutes; the sextet built around him toured until 2008. In 2007 the brothers' own label, B-Flat Recordings, issued the first album by the Belgian drummer Dré Pallemaerts, and on saxophonist Samy Thiébault's debut that year Stéphane was heard on record as a drummer for the first time. In 2008 the brothers turned to Brazilian song with Milton Nascimento, backed by Éric Legnini, Bramerie, Ceccarelli and strings from the Orchestre National d'Île-de-France. That December he and Lionel spent five days at the Studio de Meudon cutting Avishai Cohen's Aurora for Blue Note, Stéphane on trumpet and flugelhorn and Lionel on flute, in a band that included Shai Maestro, Amos Hoffman and Itamar Doari.

Since 2011 he has recorded mostly in small, exposed formats. The Same As It Never Was Before put him in a quartet with Kirk Lightsey, Sylvain Romano and Billy Hart. Ever After (2013) kept Lightsey, added Jacky Terrasson on Fender Rhodes, Johnathan Blake on drums and a string quartet, and gave two tracks to the singer Gregory Porter. Love For Chet (2015) is a trio with guitarist Jesse van Ruller and Bramerie; Mother (2016) a duo with Terrasson for Impulse!; 2.0 (2019) a second duo album with Sylvain Luc, on which Belmondo picks the accordion back up for one Philippe Sarde piece. The Belmondo Quintet returned in 2021 with Brotherhood, recorded in January 2019 and dedicated in part to their father, and took the Académie du Jazz's Prix du disque français. He has since made QR Code II (2024) with pianist Thierry Maillard, whose "Hagaldia" is an homage to Sylvain Luc, and duo records with Antonio Faraò and with Dado Moroni, the latter taped live at the Jazz en Tête festival in Clermont-Ferrand in October 2025. Since 2001 the trumpet and flugelhorn he plays have been his own: Henri Selmer Paris markets the models he helped develop as the "Concept TT".

Belmondo is a lyric player first, and the flugelhorn is at least as much his instrument as the trumpet: several of his most admired records, Hymne au Soleil and ameskeri among them, credit him on flugelhorn alone. The sound is warm, unhurried and immediately identifiable, built on a long breath rather than on speed, and it has made him a natural duo partner, a format he has returned to with Sylvain Luc, Jacky Terrasson, Thierry Maillard and Dado Moroni. Gil Evans, whom he played under at twenty, is the influence he names first, and Evans's habit of writing for unorthodox wind colours runs straight through the Belmondo brothers' own projects, which routinely add oboe, bassoon, English horn, French horn and tuba to a jazz rhythm section. Chet Baker is the other pole, audible in the vibrato-light phrasing and acknowledged outright on Love For Chet. His willingness to work outside the standard repertoire is unusual for a player of his idiom: a whole album of Stevie Wonder songs, another of Lili Boulanger and Fauré reorchestrated for winds, a Brazilian record with Milton Nascimento, a Grateful Dead project with Lionel. French critical recognition has been emphatic and repeated, running from the Académie du Jazz's Prix Django Reinhardt in the mid-1990s through three consecutive years of Victoires du Jazz for Hymne au Soleil, Wonderland and Influence, to the Prix du disque français for Brotherhood in 2021.