Simpson was born in Edinburgh 2 April 1854. She was the daughter of William Simson (1811–1858), secretary of the Bank of Scotland, and Jane Christiana Aberdein (b. 1820) and was one of nine children. She lived with her family in Eton Terrace, New Town, for much of her life.
Frances Simson was the eldest, at 38 years of age, of the all the women who graduated in Masters of Arts, made possible by the Universities (Scotland) Act of 1889. Simson had enrolled in 1867 to degree classes delivered by the Edinburgh Association for the University Education of Women (EAUEW; formerly the Edinburgh Ladies' Educational Association, ELEA, founded in 1867).
Together with Margaret Nairn, Elsie Inglis, Frances Melville and Chrystal Macmillan, Simson petitioned the right for five women graduates to vote for the university MP at the general election of 1906 to no avail. They also failed an appeal November 1907, so rallied to raise £1000 to support mounting their case to the House of Lords in November 1908 where Macmillan opened and performed as senior counsel, with Simson making general argument and closing the case on 12 November.
In October 1933, the year University of Edinburgh celebrated its 350th anniversary, Simson was awarded an honorary degree of LLD, as the only woman graduand, recognising her responsibility in the university education of women. Later that year, at the time she was president of the Edinburgh Equal Citizenship Society she was honoured in a luncheon held at the site of the former Caledonian Hotel on Princes Street, Edinburgh. Lady Alexandra Watson, Dame Sarah Siddons, Dr. Frances Melville, Professor E.T. Whittaker, and Dr Marion Gilchrist where among, hundred-plus guests that attended the event in honour of her work campaigning for women's education.
- "Oxford Dictionary of National Biography". www.oxforddnb.com. Retrieved 2016-02-17.
- Leneman, Leah (1995). A guid cause: The women's suffrage movement in Scotland. Mercat. p. 270. ISBN 1873644485.
- Edinburgh Association for the University Education of Women, 1867-1967. William Bishop, Market Street. Edinburgh. p. 17.
- "DR FRANCES H. SIMSON: Woman Pioneer Honoured EDINBURGH LUNCHEON". The Scotsman. 2 November 1933. Retrieved 18 February 2016.