Reading the verse above:
"Tho' I am forsaken, yet she is forsworn,
Yet she is mistaken if she think that I'll mourn,
I'll set as slightly by her as e'er she did me,
And for ever will deny her, let her go, farewel she."

Had me reaching for my dictionary to check the relationship between 'cuckoo' & 'cockold'. Collin's states the latter is derived from the French for cuckoo.

Also brought to mind was:

The elephant is a curious bird.
It flits from bough to bough.
It makes its nest in rhubarb trees
And whistles like a cow.

Cheers
Nigel