[3] At age 9 he performed for the first time on an album with his brothers (Elgarrekin), and played in the first part of a concert of Joe Dassin with a local group.

At age 15, Luc formed a jazz group called the "Bulle Quintet," and quickly gained recognition.

In 1988, he settled in Paris and became an arranger, composer and accompanist to many different French artists, including Catherine Lara, Michel Jonasz, all while being the bassist for the Richard Galliano trio.

In 1999, he founded Trio Sud with André Ceccarelli and Jean-Marc Jafet, an ensemble with which he received the French Music Award for Jazz as best group of the year in 2003.

Among the musicians he played with are Al Jarreau, Dee Dee Bridgewater, Michel Legrand, Erkan Oğur, Richard Bona, Steve Gadd, Biréli Lagrène, Renaud Garcia-Fons, Elvin Jones, Wynton Marsalis, Stéphane Belmondo, Manu Katché, Michel Portal, Bobby Thomas Jr., Andy Sheppard, Jacky Terrasson, André Ceccarelli, Jean-Marc Jafet, Alain Caron, Didier Lockwood, John McLaughlin, Bernard Lubat, Lokua Kanza, Richard Galliano, Steve Lukather, Billy Cobham, Victor Bailey, Dario Chiazzolino, Larry Coryell, Al Di Meola, and Tommy Emmanuel.

Luc died of a heart attack on 13 March 2024 on Charles Friedel street in the 20th arrondissement of Paris at the age of 58.

Luc mostly played fingerstyle, even with a steel string guitar, and sometimes used a plectrum, often switching during the course of a single song.