Born in St Kilda, Melbourne, Australia, Florance was a frequent guest star in various television series during the 1960s and was a regular on the Bellbird series. In the 1970s she began appearing in films, most notably Petersen (1974), End Play (1975), The Devil's Playground (1976), and Mad Max (1979).

In 1979 she joined the cast of the television series Prisoner (known outside of Australia as Prisoner: Cell Block H), which was produced by The Reg Grundy Organisation. As the recalcitrant, alcoholic, convicted murderer Lizzie Birdsworth, Florance became one of the show's favourite performers. The writers initially devised the character as comic relief, however with Florance's performance the character was further developed and given more substantial dramatic storylines. Her popularity was such that she won two Logie Awards as Australia's most popular television actress in 1981 and 1983. Florance left the show in 1984 and worked in such films as Nirvana Street Murder (1990).

In a heated on air exchange with Grundy's senior Vice President Peter Pinne on a live British television programme Open Air in 1989, Florance was highly critical of the production company and its treatment of the cast.

Her final film role was in A Woman's Tale (1991). As a genteel, elderly woman, down on her luck, who reminisced with her nurse of better days, while dying of cancer, Florance gave a performance that was widely praised both within Australia, and internationally following the film's release. Florance herself was fighting cancer during the filming. She won the Australian Film Institute Award for Best Actress in a Leading Role for her work, and seven days after receiving the award, died from the disease, in Melbourne.