Early in his studies he was able to hear on stage such artists as Thad Jones, Count Basie, Charles Mingus, Bill Evans, Sonny Stitt and Stan Getz live at the Nice Jazz Festival, who all had a profound impact on his future.

Amsallem started gigging in 1976 at the age of fourteen, and by high school was playing in dance bands throughout the Cote d'Azur and featured in the INA documentary La Leçon de Musique as a student of John Lewis.

He then played or collaborated with Gerry Mulligan, Joe Chambers, Gary Peacock, Bill Stewart, Joshua Redman, Maria Schneider, Jerry Bergonzi, Charles Lloyd, Bobby Watson, Roy Hargrove, Kevin Mahogany, Ravi Coltrane, Bob Brookmeyer, Bob Belden, Sonny Fortune, Tim Ries, Gary Bartz, Rick Margitza, Joe Roccisano, Blood, Sweat & Tears, and Harry Belafonte.

His composition Nuits for String Orchestra and Jazz Quartet has been performed in various soloists including Bireli Lagrene, Philip Catherine, François Theberge & Don Menza.

Amsallem returned to France in 2001, settling in Paris, where he has collaborated or recorded with local greats Stephane Belmondo, Elisabeth Kontomanou, and Sara Lazarus.

In 2019, his new quartet, featuring Cuban saxophonist Irving Acao, released "Gotham Goodbye" for the jazz&people label, to unanimous critical acclaim.