Born in Oklahoma, Franklin attended Fisk University and then Harvard University, receiving his doctorate in 1941. He was a professor at Howard University, and in 1956 was named to head the history department at Brooklyn College, part of the City University of New York. Recruited to the University of Chicago in 1964, he eventually led the history department and was appointed to a named chair. He then moved to Duke University in 1983, as an appointee to a named chair in history.