He was born in Southleigh, Oxfordshire in England and emigrated to the United States at age 18. In 1834 he got a job at the Locks and Canal Company of Lowell, Massachusetts and became Chief Engineer in 1837. He remained at the company for his entire career.
Francis originated scientific methods of testing hydraulic machinery and was a founding member of the American Society of Civil Engineers and its president in 1880. He is probably most famous for having invented the Francis turbine, which was a more efficient successor to the Boyden turbine of Uriah A. Boyden which was first demonstrated at Lowell.
Specifically in the city of Lowell, he also ordered the construction of the Great Gate over the Pawtucket Canal in 1850. Although the city was largely protected from the Merrimack River due to its elevation, a serious flood could theoretically overflow the canals running through the city. "Francis' Folly" as the gate was first known, has saved the city of Lowell from devastating floods in 1852, 1936, 1938, 2006, and 2007 by preventing the Merrimack River from entering the canal system. However, arson damage to the wooden gate in the 1970s, and the difficult method of dropping it (by breaking a large chain link) prompted the city to use a more modern steel-beam bulkhead in its place in 2006 and on.
Francis was also responsible for the construction of the Northern Canal and Moody Street Feeder. These two canals, built in the late 1840s and early 1850s, completed the 5.6 mile long Lowell canal system, and greatly increased its industrial power.