Capuçon was born in Chambéry, France, on September 3, 1981. He began playing the cello at age four and the piano at seven. He enrolled at the École Nationale de Musique de Chambéry, where he studied both instruments. In his teens he studied at the Conservatoire National Supérieur de Musique de Paris, where his teachers included Annie Cochet-Zakine. After his 1997 graduation, he enrolled for further study at the Conservatoire National Supérieur de Musique de Paris for three more years, with, among others, cello pedagogue Philippe Muller.
While a student there Capuçon played cello in the European Union Youth Orchestra and the Gustav Mahler Jugendorchester, and in 1999 he captured first prize in the André Navarra International Cello Competition. After graduation in 2000 Capuçon had further studies with Heinrich Schiff
in Vienna. By then he was an active performer on the concert scene in Europe, appearing with major orchestras and conductors.
Among his earliest recordings were a pair of acclaimed CDs: Haydn Concertos No. 1, 2 & 4 with Daniel Harding
and the Mahler Chamber Orchestra
on EMI, and, with his brother, a Virgin Classics album of duets entitled Face À Face featuring works by Kodály
, and others. In 2007 Capuçon married Delphine Borsarello, also a talented cellist. Capuçon's newer recordings include the 2008 Virgin Classics CD of sonatas for cello and piano by Prokofiev