Francis Hiram Arms was born around 1834 in Hebron, Connecticut, to Hiram P. Arms and Lucy Ann Wadhams. His mother died on July 3, 1837, and his father remarried the following year. He attended school in Norwich, Connecticut, and he married Emily Meekins on January 3, 1860. She apparently died in the early 1860s.
In 1864, he received an appointment as an acting assistant paymaster in the United States Navy. He served until January 26, 1866. He married Grace Turner on April 11, 1865, and they had at least three children: Frank, born around 1867; Alice, born on June 3, 1876; and Guy, born on April 5, 1882. They lived in New London, Connecticut. He returned to the navy in August 1866, receiving an appointment as a passed assistant paymaster. He was promoted to paymaster in 1871. The family moved to Boston, Massachusetts, in the 1870s. He died on March 16, 1889, when the USS Vandalia sank near Apia, Samoa.