Sir Francis Popham KB (1646–1674), of Littlecote House, Wiltshire and Houndstreet, Somerset, was an English politician. He was the eldest surviving son of Alexander Popham of Littlecote. He was a Member (MP) of the Parliament of England for Bath from 1669 to 1674. He succeeded his father in 1669 and was made a Knight of the Bath the same year. He married Helena, the daughter and heiress of Hugh Rogers of Cannington, Somerset and had a son, Alexander and a daughter.