Robartes was the fourth son of John Robartes, 1st Earl of Radnor and his second wife Letitia Isabella Smythe (1630–1714). He was baptised at Lanhydrock in Cornwall on 6 January 1650. He was at school at Chelsea under Mr Cary and was admitted at Christ's College, Cambridge on 2 May 1663 aged 13. Robartes was known as a musical composer and a writer on the theory of sound. He became a Fellow of the Royal Society in 1673.
In 1673, Robartes was elected Member of Parliament for Bossiney in the Cavalier Parliament and sat until 1679. He was elected MP for Cornwall in 1679 and sat until 1681. He was elected for Cornwall again in 1685 and sat until 1687. In 1689 he was elected MP for Lostwithiel and sat until 1690 when he was re-elected for Cornwall. He was elected MP for Tregony in 1695 and sat until 1702 when he was elected MP for Bodmin. He sat for Bodmin until 1708, for Lostwithiel again from 1709 to 1710 and for Bodmin from 1710 to 1718. He was a Teller of the Exchequer from 1704 to 1710.
Robartes became a vice-president of the Royal Society. He was the brother of Robert Robartes and Hender Robartes. Robartes married firstly Penelope Pole, daughter of Sir Courtenay Pole, 2nd Baronet and Urith Shapcote, but had no issue. He married secondly Lady Anne Fitzgerald, daughter of Wentworth Fitzgerald, 17th Earl of Kildare and Lady Elizabeth Holles, and widow of Hugh Boscawen of Tregothnan, and their son, John, inherited the title of 4th Earl of Radnor.
|Richard Robartes, 1st Baron Robartes|
|John Robartes, 1st Earl of Radnor|
|John Hender of Botreaux Castle|
|Sir Thomas Smythe|
|Sir John Smythe|
|Robert Rich, 1st Earl of Warwick|
|Penelope Devereux, Lady Rich|
- "Robartes, Francis (RBRS663F)". A Cambridge Alumni Database. University of Cambridge.
- History of Parliament Online - Robartes, Francis
- Robartes, Francis (1710). "Concerning the Proportion of Mathematical Points to Each Other. By the Honourable Francis Robartes Esq; Vice-President of the Royal Society". Philosophical Transactions of the Royal Society. 27: 325–336, 470–472. Bibcode:1710RSPT...27..470R. doi:10.1098/rstl.1710.0050.