Fournier was born in New Orleans, Louisiana into a Creole family. He left college to join a big band led by King Kolax. After Kolax downsized to a quintet, Fournier moved to Chicago in 1948, where he played with such musicians as Buster Bennett, Paul Bascomb and Teddy Wilson. As house drummer at the Bee Hive club on Chicago's South Side in 1953-55, he accompanied many visiting soloists, including Lester Young, Ben Webster, Sonny Stitt, J.J. Johnson, Earl Washington and Stan Getz.
From 1953 to 1956, he also worked many recording sessions with Al Smith, Red Holloway, Lefty Bates, and others. He joined Ahmad Jamal’s trio in 1957, along with bass player Israel Crosby, and remained with the group until 1962, appearing on a series of recordings for the Chess label. The best known of these, At the Pershing: But Not for Me (1958), became one of the best selling jazz records of all time, remaining on the Billboard jazz charts for over two years.
After leaving the Jamal trio, Fournier joined George Shearing for two years before rejoining Jamal briefly in 1965-66. He then took a long-running gig with a trio at a restaurant owned by Elijah Muhammad.
He worked with Nancy Wilson, Clifford Jordan, Billy Eckstine and Joe Williams, John Lewis and Barry Harris. Fournier was also a teacher of drumming, working at Barry Harris’s Jazz Cultural Theater, the New School, and the Mannes College of Music.
A stroke in 1994 made him a wheelchair user and unable to play drums, but he continued his teaching activities. He died from a cerebral hemorrhage in Jackson, Mississippi, in 2000.
With Gary Burton
- 3 in Jazz (RCA, 1963)
With Ahmad Jamal
- At the Pershing: But Not for Me (Argo, 1958)
- Jamal at the Penthouse (Argo, 1959)
- Happy Moods (Argo, 1960)
- Listen to the Ahmad Jamal Quintet (Argo, 1960)
- Ahmad Jamal's Alhambra (Argo, 1961)
- All of You (Argo, 1961)
- Ahmad Jamal at the Blackhawk (Argo, 1962)
- Poinciana (Argo, 1963)
- Extensions (Argo, 1965)
- Rhapsody (Cadet, 1965)
With Sam Jones
- Down Home (Riverside, 1962)
With Clifford Jordan
With Jimmy Reed
- "Ain't That Lovin' You, Baby" (Vee-Jay, 1953)
With George Shearing
With Frank Strozier
- Cloudy and Cool (Vee Jay, 1960) - with Billy Wallace and Bill Lee