Baptiste Trotignon, the 37-year-old jazz pianist from Paris, was the original inspiration for the Partager festival at London's Vortex and Charlie Wright's clubs – an event that has recently been joining American, French and British musicians in combinations they don't usually attempt. Partager means share, which happened to be the title of an ambitious album Trotignon made with downtown New York stars in 2009. The closing night of the festival at the Vortex, featuring two exploratory improvising duos, was an absorbing lesson in how spontaneous musical sharing works.

Trotignon has applied a jazz sensibility to his own piano concertos, and to interpretations of music from Led Zeppelin and Dylan to Edith Piaf. But in conversation with the vivaciously Hagrid-like Argentinian percussionist Minino Garay, he mixed steadily building originals somewhat reminiscent of the slow-burn themes of Brad Mehldau with a seductive tango from the percussionist's homeland, the north African world-jazz of flautist Magic Malik, and an account of A Night in Tunisia that gave this classic bop theme a lurchingly arrhythmic, fitfully Latin-jazzy character. The remarkable Garay used shakers, tom-toms and the cajón box-drum to impart a drum-choir sonority and depth, but at times also a lightness that suggested the most subtle of conventional kit-players. Trotignon constantly unfolded absorbing stories in his solos, full of startling chordal exclamations, plaintively romantic lyricism and – on Garay's delicious tango clasico – a collage of liquid lines and stuttering drumlike invitations to his partner that brought the room to rapt attention.

Trumpeter Tom Arthurs, sharing the second set with another French pianist, Denis Badault, achieved the same result with an improv-oriented music of considerably more spikiness. But Arthurs's gleaming sound and clarity of line, and Badault's abstract pluckings hooked to craggy Thelonious Monkish chordwork, established narratives that had all their own kind of edgy logic.