mcbeth was born in ropesville, texas (near lubbock). his parents were joseph phinis mcbeth, a baptist minister, and lillie may carpenter mcbeth. mcbeth had a brother, harold, and a sister, laura fay. he had an early start to his musical training, studying piano with his mother and taking up the trumpet in the second grade. he graduated from irving high school in irving, texas where he served as president of the ihs senior class of 1951, as well as president of future farmers of america. he lettered in football and track and was a member of the tiger band and choir. mary sue white mcbeth, wife of francis, was also in the irving high tiger band class of 1951. he attended hardin-simmons university in abilene, texas. while an undergraduate at h-su, mcbeth played in the university band. from december 1952 to january 1953, the band traveled with u.s. camp shows to europe. he also played string bass in a jazz combo, which was unusual for the time period due to widespread segregation throughout the south.