Abby -
Your "Reynard" is basically the same version as mine. The notes I have scribbled down on my song sheet are:

From the Joyce Collection, Old Irish Folk Music and Song, republished 1965. Patrick Weston Joyce (1827-1914) was an Irish collector and author of many books on Irish culture. Old Irish Folk Music and Song was originally published in 1909, and his Ancient Irish Music was published in 1906, both by Longman, Green & Co.

That said, since I borrowed this book to copy out the song in 1976, I'm not really sure I knew (at the time) enough to write down the proper information! If anyone has access to these books, perhaps they can confirm my scribbled notes.