Franklin Ashley was born in 1834 in Auburn, Ohio, to Ebenezer and Mary Ashley. His father died in 1843, and his mother remarried the following year. His stepfather died in 1850. Ashley grew up and attended school in Auburn, and by the early 1860s, he was working as a farmer.
He enlisted in the Union army on November 4, 1861, and he mustered in as a private in Company H of the 64th Ohio Infantry. The regiment took part in the Battle of Shiloh, the siege of Corinth, the Battle of Perryville, the Battle of Stones River, the Battle of Chickamauga, the Atlanta campaign, and the Battle of Nashville. In August 1864, he condemned Peace Democrats as "the bigest sinners on the face of the earth." He accused them of undermining the Union war effort and prolonging the conflict. He added that, "when I think of...how many brave boys are loosing their lives for their country and they [Peace Democrats] doing all they can against them it hurts my feelings." He was promoted to corporal in May 1865, and he mustered out on December 3, 1865.
He married Celesta A. Ewing on February 25, 1864, and their daughter Carrie was born around 1866. His wife died in 1868. By 1870, he was living in his father-in-law’s household in Shelby, Ohio. He married Sarah E. Ewing—his first wife’s sister—on June 24, 1873, but she died in 1875. He eventually returned to Auburn. He applied for a federal pension in March 1893 and eventually received one. By 1920, he was living in his daughter’s household in Sharon, Ohio. He died in Richland County, Ohio, on May 7, 1926.