Furneaux was born Elisabeth Yvonne Scatcherd and came to England in 1946 to study Modern Languages at St Hilda's, Oxford, where she was known as "Tessa Scatcherd". She began her acting career in England in 1952 with a few minor productions. Later she participated in many great international productions and worked with famous actors and actresses, such as Catherine Deneuve in the movie Repulsion (1965). Later, she married Jaques Natteau, who died on 17 April 2007, leaving Furneaux a widow. Now she is retired from her acting career and lives in Lausanne, Switzerland.