Joseph was born in 1870 in Liverpool. After a number of varied jobs he became a stockbroker, joined Settle, Speakman & Company and became the chairman and managing director.
He was a member of Liverpool City Council from 1903 until 1913. During the First World War he worked at the War Office becoming an assistant secretary at the Ministry of National Service.
Joseph was appointed a Commander of the Order of the British Empire (CBE) in 1918 and in 1922 he was knighted. He was a director of many public companies including the Midland Bank and from 1937 to 1940 was a member of the Royal Commission on the Location of Industry. He was appointed the High Sheriff of Staffordshire for 1932. Sir Francis was promoted to Knight Commander of the Order of the British Empire in 1935 and created a baronet in 1942.
He died on 8 February 1951