Francis M. Kelly was born around 1833 in New York. He eventually moved to Ohio, and he married Phebe Eaton on July 19, 1856. They had at least two children: Eugene, born around 1860; and Francis, born around 1864. They lived in Scipio, Ohio, and Kelly worked as a sawmiller. By 1860, he owned $1,000 of real estate and $50 of personal property.
He enlisted in the Union army on May 20, 1861, and he mustered in as a corporal in Company C of the 23rd Ohio Infantry. The regiment took part in the Battle of Antietam and the Shenandoah Valley campaign. He was promoted to sergeant on June 17, 1862, and to 2nd lieutenant on January 14, 1864. He mustered out on July 26, 1865.
He settled in Reed, Ohio, after the war, and he earned a living as a carpenter. By 1870, he owned $200 of personal property. He died of heart disease on April 3, 1894.