Jacques Georges Coursil was born on March 31, 1938, in the 18th arrondissement of Paris, to parents from Fort-de-France, Martinique. He began on the violin at nine and moved to the trumpet as a teenager. His early listening ran from Webern and Schoenberg to New Orleans jazz and the Martinican biguine.

In 1958 he left France for Mauritania and then Senegal, and spent about three years in West Africa, where he became a friend of Léopold Sédar Senghor. He came back to France in 1961 to teach and study. After the assassination of Malcolm X in 1965 he moved to New York and stayed until about 1975. There he studied piano and composition with Jaki Byard and Noel DaCosta, worked at the Dom (later the Electric Circus) and rehearsed with Sun Ra's band. He taught French and mathematics at the United Nations International School, where the future composer John Zorn was one of his students.

His first recording session was drummer Sunny Murray's ESP-Disk album Sunny Murray (1966), with the saxophonists Byard Lancaster and Jack Graham and the bassist Alan Silva. In 1967 he played trumpet on Your Prayer, the ESP-Disk quintet record by saxophonist Frank Wright with the altoist Arthur Jones, the bassist Steve Tintweiss and the drummer Muhammad Ali. On May 12, 1967 he was one of two trumpeters, with Warren Gale, in a long free improvisation with the clarinettist Perry Robinson, Tintweiss and the drummer Laurence Cook that remained unreleased until 2021, when it came out as Ave B Free Jam. He also played in groups led by the trumpeter Bill Dixon.

In the summer of 1969 he was in Paris and made three sessions for the BYG label at Studio Saravah. On June 9 he played on pianist Burton Greene's Aquariana; on June 10 he recorded his own Black Suite, a two-part piece with Anthony Braxton on contrabass clarinet, Greene on piano, Arthur Jones on alto saxophone, Beb Guérin on bass and Claude Delcloo on drums; and on July 7 and 8 he led Jones, Guérin and Delcloo on Way Ahead, issued under the name Jacques Coursil Unit. Both of his own albums came out in BYG's Actuel series.

Born in Paris, he lived and worked in France from about 1975 onward, apart from a long stretch in Martinique and visiting posts abroad. He turned to scholarship and took two doctorates at the Université de Caen, in 1977 and 1992, teaching literature and theoretical linguistics there. In 1995 he took a post in Martinique at the Université des Antilles et de la Guyane, and in the early 2000s he was a visiting professor at Cornell University and also taught at the University of California, Irvine. His books include La Fonction muette du langage (2000) and Valeurs pures: Le paradigme sémiotique de Ferdinand de Saussure (2015), and he was recognized as an authority on Saussure and on the writer Édouard Glissant. For some 35 years he made no records.

He came back to music in 2004 and 2005. Minimal Brass was performed in November 2004 in New York and released on Zorn's Tzadik label in April 2005: a single piece of overdubbed trumpet fanfares built on circular breathing, a technique he learned from the trumpeter Jimmy Owens. In 2006 he played on the track "L'Un et le multiple" on the rapper Rocé's album Identité en crescendo. Clameurs (Universal Music France, 2007), recorded in Fort-de-France in 2006, sets trumpet against voices in four oratorios on texts by Monchoachi, Frantz Fanon and Édouard Glissant and a song of Antar. Trails of Tears (Sunnyside, 2011), recorded in Martinique, New Jersey and Montreuil between 2007 and 2009, takes the forced removal of the Cherokee people as its subject and adds a free-jazz group on its fourth piece: Perry Robinson, Mark Whitecage, Bobby Few, Alan Silva and Sunny Murray. A 2012 DVD, Photogrammés, filmed by Guillaume Dero, shows him in concert, in conversation and playing a duo with Archie Shepp. In November 2011 he recorded FreeJazzArt (Sessions for Bill Dixon) with Alan Silva in Alfortville, issued by RogueArt in 2014, and in 2017 he received the Édouard Glissant Prize for his body of work. His last album, Hostipitality Suite, a pair of side-long pieces for trumpet and speech, appeared on SAVVY Records in 2020.

Jacques Coursil passed away on June 26, 2020, in Plombières, Belgium, at the age of 82. He was survived by his wife and two children.

Coursil was one of the few European players in the New York free-jazz scene of the 1960s, and his own records of 1969 are credited to him as composer and arranger: Black Suite and Way Ahead are built as side-long pieces for a small group with alto saxophone, bass and drums. After his return he moved away from the group format toward solo trumpet and spoken or sung text. Minimal Brass uses overdubbing and circular breathing to build fanfares from a few notes, and the oratorios of Clameurs and Trails of Tears pair the trumpet with poetry, Creole and French voices and the history of slavery, colonialism and the Americas. He named Webern, Schoenberg, New Orleans jazz and biguine among his early influences, studied with Jaki Byard and Noel DaCosta, and learned circular breathing from Jimmy Owens. The New York and BYG records belong to free jazz; the later oratorio and fanfare records sit at its avant-garde edge.