Paducah is located south of the center of Cottle County. According to the United States Census Bureau, the town has a total area of, all land. Three U.S. highways intersect in the center of town. U.S. Route 83 leads north to Childress and south to Guthrie, while U.S. Route 70 leads east to Crowell and west to Matador. U.S. Route 62 follows US 83 north out of town and US 70 to the west.
As of the census of 2000, there were 1,498 people, 650 households, and 421 families living in the town. The population density was 985.0 people per square mile. There were 820 housing units at an average density of 539.2 per square mile. The racial makeup of the town was 79.57% White, 11.21% African American, 7.61% from other races, and 1.60% from two or more races. Hispanic or Latino of any race were 20.29% of the population. There were 650 households out of which 28.0% had children under the age of 18 living with them, 49.7% were married couplesliving together, 12.3% had a female householder with no husband present, and 35.1% were non-families. 34.0% of all households were made up of individuals and 23.5% had someone living alone who was 65 years of age or older. The average household size was 2.25 and the average family size was 2.86. In the town, the age distribution of the population shows 24.0% under the age of 18, 6.0% from 18 to 24, 20.3% from 25 to 44, 23.0% from 45 to 64, and 26.6% who were 65 years of age or older. The median age was 45 years. For every 100 females, there were 82.2 males. For every 100 females age 18 and over, there were 78.4 males. The median income for a household in the town was $23,333, and the median income for a family was $30,652. Males had a median income of $26,184 versus $16,131 for females. The per capita income for the town was $15,778. About 15.4% of families and 20.4% of the population were below the poverty line, including 30.0% of those under age 18 and 17.8% of those age 65 or over.
William S. "Bill" Heatly, a Democratic member of the Texas House of Representatives from 1955–1983, known as the "Duke of Paducah". A sculpture of his bust is located on the west side of the Cottle County Courthouse. Heatly's son, William H. "Bill" Heatly, previously served as District Judge for the 50th Judicial District with his home base in Paducah.
