Dr Bennett was born at Fairview, and educated at Timaru Boys High School. He trained at Otago Medical School, graduating in 1925. He became a house surgeon at New Plymouth Hospital following which he entered general practice. In 1933, he moved to Christchurch, and while still engaged in general practice he submitted an essay on his experiences in obstetrics, for which he was awarded the Hunterian Society's gold medal in 1935, this being the first occasion on which it had been awarded outside the United Kingdom.

In 1936, Dr Bennett was appointed to the honorary staff of the Christchurch Hospital as assistant physician and anaesthetist. He was appointed physician on his return from post-graduate study in London and Aberdeen in 1948. He took part in intern teaching at the bedside for which he drew on his general experience. He also helped to establish the Canterbury Medical Library and a clinic for alcoholics. He became president of the Canterbury Division of the New Zealand Medical Association. In 1918 and 1919, Dr Bennett served in the medical corps during the First World War. In World War II he served in New Caledonia and the Solomon Islands. He reached rank of lieutenant-colonel and was awarded the Member of the Most Excellent Order of the British Empire (MBE Mil).

Dr Bennett had considerable literary talent. He wrote a centennial history of Christchurch Hospital under the title 'Hospital on the Avon: the History of the Christchurch Hospital 1862-1962'. His other works include: 'The Tenth Home' published in 1966,'The March of the Little Men' in 1971 and 'A Canterbury Tale: the Autobiography of Dr Francis Bennett', completed just before his death. He had a number of contributions of a historical nature accepted by the 'New Zealand Medical Journal'.

Dr Bennett married Pearl Allen Brash, and they had three sons and two daughters. He was a humble man whose manner hid a depth of knowledge and understanding of people. It was characteristic of the man that he gave instructions for the future care of his patients, discussed with his wife his funeral arrangements and then, having completed his last book, departed from a full and rewarding life.