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Couturier began learning piano at the age of six. A year after earning in 1977 his degree in classical piano and musicology, he met in Jacques Thollot's quartet the bassist Jean-Paul Céléa, with whom he formed a duo. Between 1981 and 1983, Couturier toured with John McLaughlin, with whom he also recorded. Over time, he played with French jazz musicians such as André Ceccarelli, Eddy Louiss, Michel Portal, François Jeanneau and with Daniel Humair. Afer first meeting during the 1985 edition of the Festival de Carthage, Couturier collaborated on Tunisian oud player Anouar Brahem's albums Khomsa (1994), Le pas du Chat Noir (2001) and Le Voyage de Sahar (2005), and the two have toured together several times since 2001.
In 2006 his album Nostalghia - A Song for Tarkovsky was released on the label ECM Records alongside soprano saxophonist Jean-Marc Larché, accordionist Jean-Louis Matinier and cellist Anja Lechner. The album is dedicated to the film director Andrei Tarkowski and his films. The album's music was also presented at various festivals, first in Bergamo in 2006. Other albums with the "Tarkovsky Quartet" followed in 2011 and 2017. In 2007, he played in the quintet "Passaggio", with which he recorded two albums on Label Bleu, and in the "European Jazz Trio" with Céléa and Wolfgang Reisinger. He also plays in duo with the violinist Dominique Pifarély on her album Poros (1997) and with the pianist Jean-Pierre Chalet. With the countertenor Dominique Visse he recorded From Machaut to Berio.
- 2014: With the cellist Anja Lechner Moderato cantabile, ECM New Series 2367, 2014.
- 1981: He received the Django Reinhardt Prize.
- Werke von François Couturier in the German National Library catalogue
- Website des Künstlers
- Biographie bei Label Bleu
- Biographie bei ECM und zu seinem Album Nostalghia
- Improvisation mit fünf Lebenslinien in FAZ vom 16.