The entry on De Fleury is in error, as noted in the website. Lewis Edson took the tune from part of Bach Cantata 212. The midi of that tune is on Cyberhymnal: How Tedious
"How tedious...." is discussed in a current thread.
I believe that Johann Sebastian Bach used the English-Irish melody for "Farewell, ye..." as a basis for one part of the Cantata (sometimes called the Peasant Cantata).
Johann Christian Bach arranged a number of Scottish, Irish and English songs, one being "Farewell, Ye Green Fields." This may be the same one J. S. used.

Uncle Jaque and I are trying to find the old secular song. It was in Madden Collected Ballads, but we don't have access to that. We are hoping some of our UK Mudcats know the old song.

It also may be the antecedent of "Green Fields of America," etc. etc. but until it is found, much posted here is guesswork!!