Frances Burney was a niece of the novelists Frances Burney and Sarah Burney, and granddaughter of the musicologist Charles Burney. One of eight children of the impecunious musicians Esther "Hetty" Burney (1749–1832) and Charles Rousseau Burney (1747–1819), who were cousins, she became a governess at the age of eighteen and worked in various such posts for the rest of her life. This included periods in the households of Sir Thomas Plumer and Sir Henry Russell.
In 1818 she published Tragic dramas; chiefly intended for representation in private families: to which is added, Aristodemus, a tragedy, from the Italian of Vincenzo Monti. These are too bombastic for modern taste. It has been speculated by the author of her ODNB entry that Burney was affected by "the concerns of her grandfather Charles Burney (1726–1814) about the potential impropriety of the stage, particularly for female dramatists." She appears not to have had a close relationship with her aunt, Frances Burney, Madame D'Arblay, who claimed in a letter to Esther, "I once thought I had caught a bit of her heart—& I tried for it, 3 or 4 years ago—but I see, & am sorry to see, my mistake."
Having suffered attacks of jaundice throughout her life, Frances Burney died in 1828 in Bath.