Franklin Barlow Sexton was born in New Harmony, Indiana on April 29, 1828 to parents, Dr. Samuel Sexton and Emily Hughes Davis. His family soon relocated to the Mexican territory of Tejas in 1831, settling in San Augistine County. Sexton attended Wesleyan College, graduating in 1846. After legislation passed in the newly formed Republic of Texas, Sexton took the Bar at the young age of 20 and opened a Law practice in his home County. He married Eliza S. Richardson on August 10, 1852 and the couple had twelve children, including a daughter, Loulie, who married Harry F. Estill. Sexton was elected as a Democrat to the Texas legislature in the 1850s and to the state Senate in 1861. In 1860, Sexton was president of the state Democratic convention.

At the outbreak of the Civil War, Sexton joined the Confederate Army and served for a short time before being elected to the Texas Senate. However, he did not return from service in time to fulfill this role. Instead, on November 6, 1862, Sexton was chosen to represent the Fourth Congressional District in the first Confederate House of Representatives. He would be re-elected in 1863, one of only two Texans to be elected both terms of the Confederate Congress. Along with being Methodist, Sexton was also a Mason. He was chosen grand commander of the Knights Templar of Texas in 1870.

After the Civil War, Sexton returned to his Law practice in San Augistine County, Texas, until a move to Marshall, Texas in 1872. He became a railroad attorney and continued his estate practice in Marshall until the death of his wife in 1894. Sexton moved to live with his youngest daughter, Mary Richardson Sexton, in El Paso, Texas. He was then appointed to be a judge on the state Supreme Court and served as a United States commissioner. Franklin Barlow Sexton died in El Paso, Texas on May 15, 1900 and is buried in Marshall, Texas. His Civil War diary was published in the Southwestern Historical Quarterly in 1935.