The musician suffered from aortic rupture suddenly and was taken to the Pompidou Hospital in Paris, said Eric Trosset.
Allen was drummer and musical director of the band Fela Kuti, Africa 70 in the 1960s and 70s, and most recently played with vocalist Blur and Gorillaz Damon Albarn as part of the supergroup The Good, the Bad and Queen.
Afrobeats, a throbbing West African style of music, was popularized by its pioneer, the late musician and political activist Kuti in the 1960s.
Kuti, described as one of the biggest stars in Africa, used his cool beats and song lyrics as comments to speak out against the military government in Nigeria at the time.
But the new generation of Afrobeats artists has gained international success and recognition through the music genre, even though they have avoided political references in their music.
Nigerian-American rapper Jidenna described Allen as “The Godfather of Afrobeat Rhythms” and said his voice changed lives.