Thompson was born in Sheffield, Alabama, on August 19, 1942, the son of Ruth Inez (née Bradley) and Fletcher Session Thompson (born Lauderdale County, Alabama, August 26, 1919, died Lawrenceburg, Tennessee, May 27, 1990), who was an automobile salesman. Thompson had English and distant Dutch ancestry. He attended public school in Lawrenceburg, graduating from Lawrence County High School, where he played high-school football. Thereafter, he worked days in the local post office, and nights at the Murray bicycle assembly plant.