Claude Jean Harry Bolling was born April 10, 1930, in Cannes, France, and grew up absorbing the American jazz records circulating in postwar France. He studied piano at the Nice Conservatory and then in Paris, and was performing professionally by age fourteen. In 1945 he assembled his first small band, modeled directly on the New Orleans jazz he had absorbed from records by Jelly Roll Morton, King Oliver, Louis Armstrong, and Sidney Bechet, and from the Duke Ellington sidemen he studied closely, including Johnny Hodges, Rex Stewart, Barney Bigard, and Cootie Williams; Ellington himself remained his single most important influence throughout his life.

Bolling's teenage years put him directly in front of visiting American jazz royalty passing through Paris's postwar club scene. In 1948 he accompanied blues singer Bertha "Chippie" Hill at that year's Grande Semaine du Jazz, and he went on to work alongside trumpeters Roy Eldridge and Cat Anderson, cornetist Rex Stewart, saxophonist Paul Gonsalves, and vibraphonist Lionel Hampton, several of them Ellington alumni. He formed his own orchestra in the mid-1950s, soon known as the Show Bizz Band, and by 1956 was leading the group that would grow into the long-running Claude Bolling Big Band. His early leader recordings, including 1955's Joue Georges Brassens Et Sidney Bechet for the French label Vogue, worked the same ragtime, stride, and New Orleans-rooted vocabulary; a 1965 quartet session credited to Cat Anderson Claude Bolling And Co., cut for Philips, paired him directly with three members of Ellington's own band: Anderson, Gonsalves, and drummer Sam Woodyard. In 1970 the Académie du Jazz recognized Bolling's traditionalist stature with its newly created Prix Sidney Bechet, honoring the year's outstanding traditional jazz musician.

Alongside his jazz bandleading, Bolling built a substantial parallel career as a French film and television composer, arranger and conductor, and, for a stretch in the 1960s, pop-music entrepreneur: he created, produced, and managed Les Parisiennes, a novelty female vocal quartet, while composing incidental scores for French cinema and television. That side of his career grew into roughly one hundred film and TV scores between 1957 and 1998 for directors including Jacques Deray, René Clément, and Philippe de Broca; his best-known score, for Deray's crime drama Borsalino (1970), was issued as a Paramount soundtrack album, and later credits included Le Magnifique (1973) and the long-running television series Les Brigades du Tigre.

Bolling's defining achievement arrived in 1975, when he began pairing his jazz piano trio with world-class classical soloists in a series of original suites written expressly for that combination. The first, Suite for Flute and Jazz Piano Trio, recorded with flutist Jean-Pierre Rampal, bassist Max Hédiguer, and drummer Marcel Sabiani, became an unlikely commercial phenomenon in the United States, earning a 1975 Grammy nomination for Best Chamber Music Performance and staying on Billboard's classical and crossover charts for years. That same year he recorded Concerto for Classic Guitar and Jazz Piano Trio with guitarist Alexandre Lagoya. Bolling repeated the formula through the following decade with a rotating cast of soloists: violinist Pinchas Zukerman on Suite for Violin and Jazz Piano Trio (1978), Rampal and Lagoya together on Picnic Suite for Flute, Guitar and Jazz Piano Trio (1980), trumpeter Maurice André on Toot Suite for Trumpet and Jazz Piano Trio (1981), and cellist Yo-Yo Ma on Suite for Cello and Jazz Piano Trio (1984).

Bolling kept his big band working throughout the same decades, recording a run of Duke Ellington tribute albums, including Bolling Band Plays Ellington (1987) and Bolling Big Band Plays Ellington: Black, Brown and Beige, recorded live in January 1989 and released in 1990. Vocalist Guy Marchand fronted the band on a 1988 live recording later reissued as Crooner's Dream, and in 1991 violinist Stéphane Grappelli made his first-ever recording with a jazz big band on First Class, released the following year, pairing swing standards with two new Bolling originals written for the occasion. France recognized Bolling's dual careers with a string of honors: Chevalier of the Légion d'Honneur in 1990, Commandeur des Arts et des Lettres in 2006, and Officier of the Légion d'Honneur in 2010. He continued performing and recording into his final years. Claude Bolling died December 29, 2020, in Saint-Cloud, France, at ninety, and is buried in Garches.

Bolling's piano style stayed rooted in stride, swing, and ragtime even as pop culture moved past it: AllMusic calls him a "kingpin in the mainland European trad jazz movement of the 1950s and '60s," and Bolling himself named Duke Ellington his primary influence alongside Teddy Wilson, Earl Hines, and Art Tatum, absorbing Fats Waller, the Count Basie Orchestra, and Willie "The Lion" Smith on the swing and stride side and, later, Erroll Garner, Thelonious Monk, Oscar Peterson, George Shearing, and Horace Silver as he expanded his harmonic vocabulary. That grounding in an older jazz language is what made his crossover suites distinctive: rather than modernizing his own playing to meet classical soloists halfway, Bolling wrote through-composed dance-suite forms borrowing from Bach and the Baroque suite, then set his trio's steady, unaltered swing feel against them. The combination made him, commercially, the most successful figure to work that vein of classical-jazz crossover, and it proved durable enough that he kept returning to the format with new soloists across three decades.