From a family of farmers (his brother was Louis Puech, Député for the Seine Department from 1898 to 1932, and Minister of Public Works from 3 November 1910 to 27 February 1911), he began as an apprentice in the marble workshop of François Mahoux in Rodez.
In 1872, after two years training, he pursued an apprenticeship in Paris in the workshop of François Jouffroy then of Alexandre Falguière and Henri Chapu, at the same time following an evening course at the Beaux-Arts.
From then on he received several official commissions from the French Third Republic, sculpting (among others) busts of Jules Ferry (1895), Charles Augustin Sainte-Beuve (1898), Émile Loubet (1901) and Benito Mussolini (1925).
He was elected a member of the Académie des Beaux-Arts in 1905, and made a knight of the Légion d'honneur on 17 January 1908.
Among those who studied with him were the American sculptors Clara Hill,[2] Ernest Keyser[3] and Helen Farnsworth Mears.