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Fleury was born in Paris. He holds a degree in mathematics and a doctorate in physics from the École Polytechnique in Paris and a Master in Theoretical Physics from the École Normale Supérieure. He worked in France for Sun Microsystems before moving to the United States where he has worked on various Java projects.
Fleury's research interest focused on middleware, and he started the JBoss project in 1999. JBoss Group, LLC was incorporated in 2001 in Atlanta, Georgia. JBoss became a corporation under the name JBoss, Inc. in 2004.
After selling his company to Red Hat, Fleury became Senior Vice President and General Manager of the JBoss Division. However, Fleury went on a "paternity leave" in January 2007, supposedly until 15 March 2007 but was widely rumored to be leaving Red Hat. On 9 February 2007, his departure from Red Hat was made public, saying Fleury "has decided to leave Red Hat to pursue other personal interests, such as teaching, research in physics, music and his family."