In 1735 he moved to Edinburgh and worked for the Edinburgh Musical Society for eight years, during which time he got married. Back in London, having fallen from fame, but a very versatile performer on many instruments, he played viola in Handel's opera orchestra and also in the summer at Vauxhall. It's possible that he also played timpani.
His daughter Jenny became a well-known actress in London and Dublin, and she cared for Francesco at the end of his life, when he had a stroke in 1772 and died three years later, sometime between 1 and 4 May 1775.
Much of his music has survived, but he's known mainly for his six recorder sonatas Op 1 and the twenty-eight Scottish airs in A Collection of Old Scots Tunes (1742), dedicated to Lady Charlotte Erskine (1720-1788), who supported Barsanti during his time in Scotland.