William Francis Cox was born on November 28, 1843, in Norway, Maine, to William and Elizabeth Cox. His father was a farmer who owned $4,000 of real estate and $2,100 of personal property by 1860. He grew up and attended school in Norway, and by 1860, he was working as a farm laborer.
He enlisted in the Union army on September 29, 1862, and he mustered in as a private in Company H of the 23rd Maine Infantry. Union officials assigned the regiment to the defenses of Washington, D.C., and Cox mustered out on July 15, 1863.
He returned to the Union army in March 1864, mustering in as a private in Company B of the 32nd Maine Infantry. The regiment took part in the Overland Campaign and the siege of Petersburg. He eventually earned a promotion to corporal, and he mustered out on December 12, 1864. Finally, on January 6, 1865, he mustered in as a private in Company F of the Maine Coast Guard Infantry. He spent the ensuing months stationed in Belfast, Maine, and he mustered out on July 7, 1865.
He returned to Norway after the war, and he married Katherine Noyes around 1868. They had at least two children: Oscar, born around 1871; and Wealthy, born around 1876. He worked as a farmer, and by 1870, he owned $1,200 of real estate and $390 of personal property. He applied for a federal pension in August 1873 and eventually received one at a rate of $10 per month. By 1890, he was suffering from rheumatism. In 1898, government officials increased his pension from $10 per month to $15 per month. In 1906, he received an increase to $24 per month. His wife died on March 12, 1922, and he died in Norway on April 11, 1926.