Doucet was born and died in Brussels. He studied for a time at the local Conservatoire, where his teacher Arthur De Greef had been a pupil of Liszt. Although his formal training was classical, he traveled to the USA around 1920 and by his return in 1923 had developed considerable talent as a jazz pianist. His left-hand technique in particular is clearly influenced by the stride piano style prevalent in New York in the early 1920s. Some of his arrangements are still played today, for instance Chopinata, a jazz tribute to several of the great works of Chopin.
Shortly after returning to Europe he became the house pianist at the popular Parisian cabaret Le Boeuf sur le Toit where he succeeded Jean Wiéner. He and Wiéner subsequently formed a piano-duet partnership which lasted on and off from 1924 until 1939. Together they performed in over 2000 concerts and made over 100 recordings of hot dance, jazz, blues and classical music, as well as a small number of sides in which they accompanied leading French chansonniers of the day. These include ten sides by the duet with Maurice Chevalier, and others, solo, with Édith Piaf and Yvonne George (Wiéner) and Jean Sablon and Germaine Sablon (Doucet).
After the war Wiéner went on to a notable career as a pianist, composer of film music and broadcaster; Doucet never entered a recording studio again and died, of chronic alcoholism according to Wiéner's autobiography, in 1950.