The son of David Gaudet and Delphine Hébert, he was born in Sainte-Eulalie and was educated there. Gaudet worked on the family farm, established a general store at Sainte-Eulalie and then established the company Alexandre Gaudet Ltée, a wholesale business, at Aston-Jonction. Gaudet was a member of the Montreal Board of Trade. He served as mayor of Aston-Jonction from 1928 to 1937 and from 1941 to 1947 and as prefect for Nicolet County from 1930 to 1932.[1]
In 1892, he married Flore Bourgeois. His daughter Françoise was a Quebec journalist.[1]
He was first elected to the Quebec assembly in a by-election held November 7, 1933. Gaudet was reelected in 1935 and was defeated when he ran for reelection in 1936,[1] losing to Émery Fleury of the Union Nationale.
He died at Aston-Jonction at the age of 90 and was buried there.[1]