Cockrell was born in
Warrensburg, Missouri, the son of Nancy (Ellis) and Joseph Cockrell, the sheriff of Johnson County. His older brother was
Jeremiah Vardaman Cockrell, who was a congressman from
Texas in the 1890s. Francis Cockrell attended local schools and Chapel Hill College in
Lafayette County, Missouri, graduating in July 1853; He studied law and was admitted to the bar in 1855, practicing law in Warrensburg until the outbreak of the Civil War. Cockrell was married three times. His first wife, Arthusa Dorcas
Stapp (1830–1859), with whom he had three sons. His second wife, Anna E.
Mann (1840–1871) of Kentucky, died of
consumption. In July 1873, he married Anna Ewing (1846–1894), the eldest daughter of Judge
Ephraim Brevard Ewing from Missouri. ==Civil War==