Franck Avitabile was born in Lyon on November 24, 1971. He started piano at nine at the Lyon conservatoire, first in a classical repertoire of Bach, Mozart, Brahms and Debussy. At seventeen he discovered Keith Jarrett and Chick Corea, had a first introduction to improvisation with Mario Stantchev, and in 1990 joined the conservatoire's jazz class. Alongside music he studied mathematics and computer science, earning a master's degree in discrete mathematics and a DEA in fundamental computer science. In 1994 he took part in the Collectif Mû, a gathering of musicians from the Mâcon area, and that summer spent three months in New York, sitting in at jam sessions at the Blue Note and Smalls, taking lessons with Fred Hersch and discovering the playing of Bud Powell.

Back in France he entered the jazz department of the Conservatoire national supérieur de musique et de danse de Paris after a competitive exam. In December 1997 he won a prize at the Vanves jazz piano competition, chaired by Martial Solal, and in 1998 he took the second Grand Prize at the Concours international Martial Solal (Ville de Paris) and a unanimous first prize at the Conservatoire. Two earlier records are listed for him, Tribute to Bud Powell (1996) and the trio album Lumières (1997), the latter with the bassist Louis Petrucciani and the drummer Thomas Grimmonprez. In 1998 Michel Petrucciani produced and artistically directed his first Dreyfus album, In Tradition, with the bassist Riccardo Del Fra and the drummer Luigi Bonafede, and Francis Dreyfus signed him to his label. All About Jazz describes him as the only musician Petrucciani produced both on record and on stage, and the record earned him a Django d'Or in 1999 as the best French debut.

Right Time (2000) paired him with the Danish bassist Niels-Henning Ørsted Pedersen and the drummer Roberto Gatto. He played the festivals at Ramatuelle and Jazz in Marciac, where Wynton Marsalis invited him, and appeared in Paris as a guest of the saxophonist Steve Grossman. He improvised on a Frédéric Botton composition for the soundtrack of Claude Berri's film Une femme de ménage. His third Dreyfus album, Bemsha Swing, was recorded at Studio Ferber in Paris on May 21 to 23, 2002, with the bassist Rémi Vignolo and the drummer Dré Pallemaerts. He also worked in electro-jazz projects, among them the Paris Jazz Quintet (Introducing, recorded in the Netherlands in October 2000, with the drummer André Ceccarelli) and the Tassel and Naturel Fillet of Soul records.

He received the Talent Jazz Adami in 2003, and in 2004 his Franck Avitabile New Trio won the Victoires du Jazz prize for French instrumental revelation of the year. That year a concert in Maubeuge with Manu Katché and the bass guitarist Pino Palladino led to him joining Katché's group Tendances, with which he gave about a hundred concerts, playing a Nord Lead synthesizer as well as piano. His two solo piano albums, Just Play (2005) and Short Stories (recorded in March 2006), each earned a Choc from Jazzman magazine. Paris Sketches (2009), made up of his own pieces, brought Palladino and Katché into the studio with him, and he was one of six pianists, with Benjamin Moussay, Pierre de Bethmann, Franck Amsallem and Manuel Rocheman, in Martial Solal's six-piano programme at Jazz à Vienne the same year.

In 2010 he was the godfather of the first Caval'Air Jazz festival at Cavalaire-sur-Mer, and later projects have taken in Chopin, Schubert and Ravel; he is a Steinway artist. He has also become the producer of Michel Petrucciani's posthumous releases: Both Worlds Live (2016), Solo in Denmark (2022, produced for release with Christian Brorsen) and, as an executive producer, The Montreux Years (2023). In 2023 he improvised on Mozart's concerto for two pianos with Makoto Ozone and the Morphing Chamber Orchestra in the cathedral of Saint-Louis des Invalides in Paris, and in 2026 he improvised on Gershwin's Rhapsody in Blue with the 55-piece OD de Côte-d'Or orchestra, conducted by Luc Bouhaben.

Avitabile came to jazz through Jarrett and Corea and by way of Bud Powell, and his first records are explicit homages to the piano tradition: All About Jazz's review of Right Time notes his debt to Powell and to the great piano masters while pointing to his own writing, and Bemsha Swing takes its name from Thelonious Monk's tune. His mentor and producer was Petrucciani. His trio records are in a modern straight-ahead idiom, and his solo albums Just Play and Short Stories are mostly his own compositions (he is credited with 16 of the 18 pieces on the second). He associates music with three-dimensional shapes, a trait of his synesthesia, and he has about 60 published compositions. Beyond the acoustic trio he plays Fender Rhodes and synthesizers and has recorded with electro-jazz groups and, in Katché's band, in a more groove-driven setting; All About Jazz's biography says he is open to every genre, including pop and classical, and he has since turned to classical repertoire and orchestral improvisation.