The only child of Sidney Godolphin, 1st Earl of Godolphin, Francis Godolphin was born in Whitehall, London, on 3 September 1678, and baptised the same day. His mother, Margaret Godolphin, died six days later on 9 September. Educated at Eton College and at King's College, Cambridge, where he took his M.A. degree in 1705, Godolphin married Lady Henrietta Churchill in March 1698, the eldest daughter of John Churchill, 1st Duke of Marlborough and Sarah Jennings. Upon the death of her father, Lady Henrietta became Duchess of Marlborough. On 23 January 1735 Godolphin was created Baron Godolphin of Helston in Cornwall. During the King's absence from Great Britain in 1723, 1725, and 1727 he acted as one of the Lords Justices of the United Kingdom. Finally, he was in office as Lord Privy Seal from 1735 to 1740. Godolphin was buried in Kensington Church on 25 January 1766, when the Earldom of Godolphin, Viscounty of Rialton, and Barony of Godolphin of Rialton became extinct. However, the Barony of Godolphin of Helston devolved upon his cousin Francis Godolphin, 2nd Baron Godolphin of Helston.