He was the son of William Frederick Wyndham (1763–1828), youngest son of Charles Wyndham, 2nd Earl of Egremont (1710–1763) and his wife Frances Mary Harford (1759–1822), the illegitimate daughter of Frederick Calvert, 6th Baron Baltimore, by Mrs. Hester Whelan.
Perhaps to his surprise, and certainly disappointment, he did not however inherit the great estate and mansion of Petworth (inherited by the 2nd Earl ultimately from the ancient and noble Percy family), which the 3rd Earl bequeathed instead to his natural son Col. George Wyndham, created Baron Leconfield in 1859.
George Francis received his first Royal Navy commission in 1799, rising to captain in 1812.
He was a prolific builder and early patron of the architect James Thomas Knowles (senior) (1806–1884) and built the following: On 14 November 1820 he married Jane Roberts (died 1876), third daughter of Rev.
William Roberts, vice-provost of Eton College; but left no surviving issue.