Faulkner County, Arkansas was formed 12 April 1873 from Pulaski and Conway counties. The Faulkner County Clerk may have genealogy records including marriage, probate, and court records starting in 1873. For county records before 1873 look in Pulaski and Conway counties.
Neighboring counties currently include Cleburne, Conway, Lonoke, Perry, Pulaski, Van Buren, and White.
There are a couple of histories and related biographies available for Faulkner County, Arkansas.
The History of Faulkner County, Arkansas by Alex McPherson at FamilySearch Books
Biographical and Historical Memoirs of Pulaski, Jefferson, Lonoke, Faulkner, Grant, Saline, Perry, Garland, and Hot Spring counties, Arkansas, comprising a condensed history of the state … biographies of distinguished citizens…, by Goodspeed Publishing Company, 1889 at Internet Archive