A student of Auguste-Alexandre Dumont and Claude Ramey, Salmson made his debut at the Paris Salon on 1859. He wond the second class medal in 1863 and in 1867, the same year he was also appointed chevalier de la Légion d'honneur. In 1876 he was asked to act as the director of the Ecole des Arts industriels in Geneva, a position at which he excelled and had a significant contribution in the success of this establishment. In 1891 he was appointed to the position of a corresponding member of the Institut de France.
His best known public statue, Handel, is housed in the Paris Opera house.