Born in 1805 as the son of an officer in the Napoleonic army, Coste went to Delfzijl, Holland with his father as a child of 8. In 1813 the French withdrew from this fortress, passing the Zuiderzee and the Rhine. Later, he would dedicate his Souvenirs to these places. He grew up in Valenciennes, where he already developed musical activities. In December 1828 he settled in Paris and made his career, giving concerts, lessons and composing. He studied harmony and counterpoint with Sor. As a member of the Société académique des Enfants d'Apollon he played in its concerts, most notably in 1843 with his Le Tournoi in the Salle du Conservatoire. He also became a member of the Freemasons lodge and participated in a concert in 1852. He entered his most important works in the Makaroff guitar competition in Brussels in 1856, where he took second prize with Grande Sérénade. Back in Paris he continued his activities but had to take an administrative job in order to support himself. He married his pupil Louise Olive Pauilhé in 1871, after the German invasion. He injured his left shoulder in 1873, just as he had in 1863. Nevertheless he continued to give concerts up to 1880, when he could no longer play due to the extreme cold that winter. A year later he was struck by a 'cerebral congesture'. He died on 14 January 1883 and was buried at the Cimetière de Montmartre.