Franklin Brockson (August 6, 1865 – March 16, 1942) was an American lawyer and politician from Wilmington in New Castle County, Delaware.

Brockson was born in Blackbird Hundred, New Castle County, Delaware.

He graduated from the Wilmington Conference Academy at Dover (later Wesley College) in 1890.

Brockson began his career as a teacher and principal in the public schools at Port Penn and Marshallton.

Brockson died at Clayton on March 16, 1942, and is buried in the Odd Fellows Cemetery at Smyrna, Delaware.