In 1906, he graduated in law from the University of Texas at Austin and returned to his home town to practice law for the following year before working with Adoue Sr. at the National Bank of Commerce (formerly known as Flippen, Adoue, and Lobit which changed when his father became president in 1892).
After his father's death by suicide in his home on June 24, 1924, Adoue succeeded him as president of the National Bank of Commerce.
From 1939 to 1947, Adoue was president of the Dallas Chamber of Commerce, which he financially strengthened, earning him the Linz Award for community service in 1943.
In 1949, he ran for mayor but lost to Wallace H. Savage, though he received the most votes as an elected council member.
During his term as a mayor which resulted in clashes between his office and a number of unions, he passed a public-works program with which the Love Field would be expanded.