1920 Achille Souchard won the gold medal at the Olympic Games in Antwerp, together with Marcel Gobillot, Georges and Fernand Detreille Canteloube in road cycling team competition. 1920 and 1922 he won the amateur race Paris - Evreux. 1922 and 1923 he became French champion in the road race in the amateurs.
1925 Souchard stepped over to the professionals. In the same year he was champion of France of the pros and won the Critérium des As well as the Giro della provincia Milano, together with Roland Bellenger. In 1926, he was two-time champion of France, in the road race and the time trial.