The "Phoebus[?] frigate Young Richard" cruises the French main with the Shannon. They encounter two merchants and "the finest frigate that did sail out of Brest." They sink all three, rescue their crews and land in Kingston where they enjoy drinks.
From ENMacCollSeeger02 album cover notes: "E.J. Moeran recorded this song from James Sutton, 'Old Larpin', of Winerton, Norfolk, in 1915. In a note to the song printed in the Folksong Journal, Ann Gilchrist suggests that The Bold Richard is an English adaptation of an American sailor's song which describes the adventures of Paul Jones' ship, Old [sic] Richard." The song is nothing like either of Laws's Paul Jones ballads (Paul Jones, the Privateer [Laws A3] and Paul Jones's Victory [Laws A4]) - BS
If we assume "Phoebus" is an error for "famous," then it is likely that Paul Jones's _Bonhomme Richard_ is indeed meant. But she never sailed with the _Shannon_; the consorts of the former _Duc de Durac_ were the _Alliance_, _Pallas_, and _Vengeance_ -- none of them in any way famous.
And this still leaves us with the curiosity of the reference to Kingston. Is this Kingston in England? In that case, the singers can hardly be telling of John Paul Jones, who fought against England. Is the reference, then, to the Quasi-War with France fought in the years before 1800? But Jones died in 1792 -- and I can't find any battle involving other ships which fits. Alternately, is it Kingston, Jamaica? Jones sailed the Carribean several times early in his career -- but as a merchant saior, not a naval captain.
In the end, I think we simply must conclude that we don't know what this is about. Probably it's mixing two or more battles. - RBW