Franklin County is a county in Arkansas. As of the 2020 census, the population was 17,097. The county has two county seats, Charleston and Ozark. The county was formed on December 19, 1837, and named for Benjamin Franklin, American statesman. Franklin County is a damp county, with alcohol sales allowed except in Prairie & Alix townships, …Franklin County is a county in Arkansas. As of the 2020 census, the population was 17,097. The county has two county seats, Charleston and Ozark. The county was formed on December 19, 1837, and named for Benjamin Franklin, American statesman. Franklin County is a damp county, with alcohol sales allowed except in Prairie & Alix townships, and limits on liquor sales in the city of Branch.