After studying percussion at the Hogeschool der Kunsten in Arnhem, Courbois left for Paris, the center of Jazz in Europe in the early 1960s. There he worked with a number of jazz giants such as pianist Kenny Drew, violinist Jean-Luc Ponty, saxophonists Eric Dolphy, Ben Webster, Stan Getz and Johnny Griffin and guitarist René Thomas.
Courbois was one of the first musicians in Europe to experiment with free jazz: In 1961 he became the drummer and leader of the (Original Dutch) Free Jazz Quartet. In 1965 he started another group, the Free Music Quintet, composed of international musicians. Its album at the ESP label has been called the best example of European Jazz. He also played and recorded with Gunter Hampel's Heartplants Group with Manfred Schoof and Alexander von Schlippenbach.
In 1969 Courbois founded the first European 'Rock-Jazz' group, Association P.C.. This famous ensemble, winner of the Down Beat Poll, existed until 1975 with Toto Blanke, Sigi Busch, different key-boarders, including Jasper van 't Hof, Joachim Kühn and Sigi Kessler. In 1982 he founded New Association with Heribert Wagner, Ben Gerritsen and Ferdi Rikkers. He has also played with the pianists Mal Waldron, and Rein de Graaff, horn players Willem Breuker, Hans Dulfer and Theo Loevendie, and Ali Haurand's European Jazz Quintet with Gerd Dudeck, Leszec Zadlo and Alan Skidmore.
In 1992 Pierre started a Quintet under his own name and for the first time in his career performed pieces, all composed by himself. This ensemble pleasantly surprised both the critics and the public with a return to the Charlie Mingus tradition - thematic, melodic ensemble jazz and an experimentation with linear improvisation. In 1999 he founded the so called "Double-Quintet" and in 2003 his famous "Five-Four-Sextet", with, to name a few, Eric Vloeimans, Ilja Reijngoud, Jasper Blom, Paul van Kemenade and Niko Langenhuijsen.
He is still playing with Jasper van 't Hof in a trio called "Cour-Hof" with Barend Courbois on bassguitar. Also with Polo de Haas in the "Gong-Duo" sometimes with Kittie Courbois as guest.
During the 1994 North Sea Jazz Festival the Bird Award, the highest award in the Dutch Jazz World, was bestowed upon Pierre. Since 2000 he is knight of the Order of Orange Nassau and in 2008 he received the VPRO / Boy Edgar Award.
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As sideman 
With Mal Waldron
- A Little Bit of Miles (Freedom, 1972)
With Joe Vanenkhuizen
- Waltz Hot (Munich, 2002)
- Ian Carr, Brian Priestley, Digby Fairweather (eds.): Rough Guide Jazz. Der ultimative Führer zum Jazz. Metzler Verlag, Stuttgart 1999, ISBN 3-476-01584-X
- Wolf Kampmann (ed.): Reclams Jazzlexikon. Reclam, Stuttgart 2003, ISBN 978-3-15-010528-3