By 1969, the AEC had augmented into the percussion-less quartet of Roscoe Mitchell, Joseph Jarman (saxophones), Lester Bowie (trumpet) and Malachi Favors Maghostut (bass). The group crossed the Atlantic Ocean and arrived in Europe to perform throughout the continent. Moye at the time was rehearsing and performing in Paris, France, at the American Center for Students and Artists, where musicians such as Art Taylor and Johnny Griffin practiced collectively. When Mitchell met with Moye again at the Center, he asked Moye to join his group, which was already known as the Art Ensemble of Chicago and had issued several recordings including three releases on the European label BYG Actual. These recordings did feature percussion but all percussion was played by Mitchell, Bowie, Favors, or Jarman.
After Moye returned to the States in the early 1970s, he played with the Black Artists Group in St. Louis, Missouri before settling in the Chicago, Illinois area. He was also in a duo with fellow percussionist Steve McCall who later was a member of Air with Henry Threadgil while still playing with the AEC. In the mid-1980s, Moye joined The Leaders, a jazz group consisting of AEC member Bowie, Chico Freeman, Arthur Blythe, Don Cherry, and Kirk Lightsey. Moye has also recorded numerous solo albums as leader of his own band. Moye toured and recorded again with the AEC in the 1990s, which was dealt a blow with the 1999 death of Bowie. Famadou Don Moye refers to his own style of drumming as "Sun Percussion". Other groups he led in the '90s include the Joseph Jarman/Famoudou Don Moye Magic Triangle Band and the Sun Percussion Summit (with Enoch Williamson), the latter of which was "a group dedicated to exploring the traditions of African-American percussion music."