Peach Orchard is a city in Clay County, Arkansas, United States. The population was 135 at the 2010 census. Peach Orchard is rooted in a…Peach Orchard is a city in Clay County, Arkansas, United States. The population was 135 at the 2010 census. Peach Orchard is rooted in an estate known as "Petit Baril," established by French explorer Pierre Le Mieux in the early 19th century. Local English-speakers were calling it "Peach Orchard" by the time Le Mieux sold the estate in 1816. A trading post operated at Peach Orchard during the mid-19th century, and was frequently raided by guerrilla forces during the Civil War.