I heard this on the Albion Band LP "Shuffle Off"; I assume it is a Branle from Claude Gervais. Odd tune, odd number of measures; definitely pushing the boundaries of Irish music. Good tune, though. Would work well on clawhammer banjo.
The first two parts are actually #4 in the "Branle de Buorgonge", page 87 of the link below; the third and fourth are #1 of "Branle de Champagne", page 93.
You can see and download the entire book here: