Eliot was born at Kew, near London, probably in 1756 (some sources suggest 1755). He died in London on 23 August 1818. His father, General Granville Eliot (sometimes Elliot) was a soldier of fortune who had served in the armies of both Austria and France, and while in France had married the Comtesse de Matigny and had several children by her. After her death General Eliot returned to England and remarried; Francis Eliot was the second son of that marriage. The two families seem to have remained in contact following General Eliot's death, and there are records of correspondence between Francis Eliot and his half-brother Antoine Xavier Eliot, an officer in the French army.
From The Biographical Dictionary of British Economists in Oxford Reference.