Francis N. Thompson was born around 1834 in Sullivan, New Hampshire, to Joshua and Abigail Thompson. His father was a laborer who owned $150 of real estate by 1850. The family moved to Hopewell, New York, sometime before 1850. He married a woman named Sarah in the late 1850s, and they had at least two children: Harriet, born around 1859; and William, born around 1861. By the early 1860s, he was working as a farmer in Hopewell.
He enlisted in the Union army on August 31, 1862, and he mustered in as a private in Company K of the 148th New York Infantry on September 5. According to his service records, he was 5 feet, 8 inches tall, with dark hair and blue eyes. The regiment took part in the Battle of Cold Harbor, and he mustered out on June 22, 1865.
He returned to Hopewell after the war. His wife probably died in the late 1860s. By 1870, he was living in his father’s household and working as a painter. He applied for a federal pension in September 1891 and eventually received one. He moved to Manchester, New York, in the late 1800s, but he returned to Hopewell by 1910. He died there on March 4, 1912.