Claude Martin was born on 5 January 1735 in the rue de la Palme, Lyons, France. He was the son of Fleury Martin (1708–1755), a casket maker, and Anne Vaginay (1702–1735), a butcher's daughter. At his local parish school he excelled in mathematics and physics. After leaving school he was apprenticed to a local silk weaver. Martin's family were middle class and by this time they had businesses in mustard, vinegar and brandy. His decision to go into the silk yarn business did therefore not go down well with his family.