Clarksville is a city in Red River County, Texas, in the United States. As of the 2000 census, the city population was 3,883. It is the county seat of Red River County. Clarksville is the birthplace of John Edward Williams, author of the National Book Award fiction co-winner for 1973 Augustus and of the novel Stoner. Clarksville City apartments for rent comparison page shows most up to date rent information on Clarksville City apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.