Savoy is a city in Fannin County, Texas, United States. The population is 712 as of the 2020 census. Savoy is located in western Fannin Count…Savoy is a city in Fannin County, Texas, United States. The population is 712 as of the 2020 census. Savoy is located in western Fannin County. Its western border is the Grayson County line. Texas State Highway 56 passes through the city, leading east 11 miles to Bonham, the Fannin County seat, and west 2.5 miles to Bells. U.S. Route 82 passes 1 mile north of Savoy, leading east to Bonham and west 16 miles to Sherman.