Jacques Schwarz-Bart was born on December 22, 1962 in Les Abymes, Guadeloupe, an overseas department of France. His mother is the Guadeloupean novelist Simone Schwarz-Bart and his father was the French-Jewish writer André Schwarz-Bart, and he spent his childhood between Guadeloupe, Senegal and Switzerland. As a child he learned the gwoka drum with the percussionist Anzala and heard the biguine of the French Antilles; at about six, in Switzerland, he discovered jazz and taught himself guitar by playing along with records. He is 63 now.

He first headed toward politics. He studied at Sciences Po in Paris and worked in the French Senate, and it was during those years that he took up the saxophone, at 24. After three years in government he left to study at Berklee College of Music in Boston, then settled in New York, where he lived in Harlem for eighteen years according to his own site. He became a sideman in the city's jazz and neo-soul circles. AllMusic describes him as an original member of Roy Hargrove's band The RH Factor, and on that group's Hard Groove (Verve, 2003) Discogs credits him on tenor saxophone on four of the fourteen tracks; English Wikipedia adds that his composition "Forget Regret" was a single from the album. The same page lists live or session work with D'Angelo, Erykah Badu, Eric Benet, Me'Shell Ndegéocello, Danilo Pérez and others, and Discogs credits him on tenor saxophone on records by Ari Hoenig, Jacky Terrasson and Etienne Charles.

His first record as leader, Immersion (Fresh Sound New Talent, 1999), was cut in New York on February 24, 1999, apart from two pieces recorded the previous December, with the pianist James Hurt and, on five tracks, Ari Hoenig on drums. AllMusic calls it a modal jazz album. In 2003 a studio group billed as The Brother Jacques Project made Inspiration (BJP Records), which shares ten of its twelve titles with the later Rise Above, with the singer Stephanie McKay, the bassist Jonathan Maron and the keyboardist Jason Lindner. In September 2003 he played in Hoenig's quartet with the pianist Jean-Michel Pilc and the bassist Matt Penman at the Fat Cat club in Manhattan, a session released as The Painter (Smalls Records, 2004), and the same group is on the DVD Kinetic Hues: Live At Fat Cat (2005).

In 2005 he left Hargrove's band, according to English Wikipedia, and began the Gwoka Jazz Project, which fused modern jazz with the drum rhythms of Guadeloupe. Its records were Soné Ka-La (2007) and Abyss (2008), both for Universal. Soné Ka-La was recorded in Brooklyn, in East Harlem and in Guadeloupe, and Discogs lists him on tenor and soprano saxophones, flute, guitar and vocals, with Lionel Loueke on guitar, Milan Milanovic on piano and guests including Admiral T and Jacob Desvarieux of Kassav' on vocals. Abyss, a tribute to his father, includes a guitar part by John Scofield and vocals by Élisabeth Kontomanou. Rise Above (Dreyfus Jazz, 2010) was made with McKay, who is also his wife, with Me'Shell Ndegéocello co-writing and playing bass on the closing track. The Art of Dreaming (Aztec Musique, 2012) is a straight quartet record with the pianist Baptiste Trotignon, the bassist Thomas Bramerie and the drummer Hans Van Oosterhout.

Jazz Racine Haïti (Motéma, 2014) turned to the rasin music and Vodou-derived songs of Haiti, with vocals by Erol Josué and Rozna Zila and a rhythm section of the drummers Obed Calvaire and Arnaud Dolmen with the bassists Reggie Washington and Ben Williams; Etienne Charles plays trumpet on two tracks. UNESCO's Slave Route programme supported the release, according to English Wikipedia. His site says he became an associate professor at Berklee in late 2016. Hazzan (Yellowbird, 2018) recasts Jewish liturgical melodies for a quartet with Grégory Privat, the bassist Stéphane Kerecki and Dolmen, with the singer David Linx on two tracks and Darren Barrett on trumpet on one; he dedicated it to his father. The same year he joined the pianist Malcolm Braff, the bassist Laurent David and the drummer Stéphane Galland on SHIJIN (alter-nativ).

He returned to the gwoka idea with Soné Ka-La 2: Odyssey (Enja, 2020 digitally, 2021 on CD) with Privat, Washington, Dolmen, the ka drummer Sonny Troupé and the singer Malika Tirolien. The Harlem Suite (Ropeadope, 2023) is a set of ten pieces for tenor and a changing rhythm section: Matt Penman on bass, Victor Gould, Sullivan Fortner and Grégory Privat on piano, and Marcus Gilmore and Terri Lyne Carrington on drums. In 2025 he and Privat released the duo record 22 on Buddham Jazz, and on August 28, 2026 he issued the trio album Resistance on Quai Son with Washington and Dolmen. He also co-produced the debut album of the group Ajoyo (Ropeadope, 2014).

Schwarz-Bart is a post-bop tenor saxophonist who bends the form toward the places he comes from: the gwoka drum patterns of Guadeloupe, the rasin music and Vodou songs of Haiti, Jewish liturgical melody, and the neo-soul and R&B he worked in around New York. AllMusic's biography sums up his sound as post-bop jazz crossed with gwo ka rhythms and R&B, and lists his genres as jazz and international, with styles including post-bop, contemporary jazz, global jazz and gwo ka. Part of his output leans toward song and Caribbean tradition, notably the vocal-led Rise Above and the gwoka and Haitian projects, but each of those records is played by a jazz quartet or trio with improvised tenor choruses, and his leader catalogue is released on jazz labels: Fresh Sound New Talent, EmArcy, Dreyfus Jazz, Motéma, Enja (Yellowbird) and Ropeadope.