Dubuisson was born on 8 August 1957, in Douai, France. As a youth, he competed in the high jump and javelin throw, with the French athletics club L'Étoile Oignies (Pas-de-Calais). After that, he switched sports, and began playing youth basketball.
During his pro club career, Dubuisson scored at least 50 points in a single French League game, on five occasions. His career-high for most points scored in a single French League game, was 55 points scored in a game against ASPO Tours, in 1989. He ended his club playing career as the French League's all-time leader in career total points scored, with 19,013.
He also holds the senior French national team's all-time record for the most points scored in a single game. On 21 November 1985, Dubuisson scored 51 points, in a 1986 FIBA World Championship Qualification game against Greece.
Dubuisson was involved in a traffic accident on 10 May 2001. He was hit by a motorcycle near his home.[10] As a result of the accident, he spent several months in a coma,[11] and had two years of intensive rehab therapy.[12] In 2005, he married the French-Bulgarian women's basketball player Madlena Staneva.[13]
His biography, Hervé Dubuisson, a Life in Suspension, was published in October 2015.[14] In 2017, a movie about Dubuisson was made. It is named The White Man Who Jumps Above Buildings. His nephew, Victor Dubuisson, is a professional golfer.[15]