Frances Clark was born Frances Noelene Denmead on 16 July 1936. She was the great grand-daughter of Frederick Thomas Brentnall (1834-1925) and Elizabeth Brentnall, née Watson (1830-1909), and a custodian of the Brentnall family archive. Frederick was a Wesleyan minister, a member of the Queensland Legislative Council, a major stakeholder in The telegraph newspaper, and a director of numerous Queensland companies. Elizabeth was state president and later honorary life president of the Women's Christian Temperance Union of Queensland (WCTU) and a prominent activist in the cause of Queensland women's suffrage.

Frederick and Elizabeth's daughter, Flora Brentnall (later Flora Harris, after she married Edgar Bridal Harris), was also a suffragist and an organiser for the WCTU, and was well-known for organising fund-raising functions for charity. She was a friend of Brisbane sculptor Daphne Mayo.

Flora and Edgar's daughter, Enid Noela Harris (later Enid Noela Denmead, after she married geologist Alan Knox Denmead), continued the tradition of charitable work and was heavily involved in the Creche and Kindergarten Association of Queensland.

Frances was one of three children of Alan and Enid Noela. She attended Brisbane Grammar School and later the Kindergarten Teachers' College (later the Kelvin Grove Teachers' College). She worked as a kindergarten teacher. She was married to Charles Quinton Clark OAM (1934-), a University of Queensland electrical engineering alumnus. Frances met Charles at a conference for the Student Christian Movement, held on the Sunshine Coast. They had four children. Frances died on 27 September 2023 in Brisbane.