Frances was the third daughter of MP and government official Daniel Pulteney (1684–1731) and first cousin once removed of William Pulteney, 1st Earl of Bath. She inherited the Earl's substantial fortune and estates close to Bath in Somerset after his death in 1764 and that of his younger brother and heir in 1767, and the Johnstones changed their surname to Pulteney. The rural Bathwick estate, which Frances and William inherited in 1767, was across the river from the city and could only be reached by ferry.