These roots, even if cognates, are not the original Indo-European word for to copulate, but Wayland Young argues that they derive from the Indo-European *bug– ("be", "become"), or as causative "create" [see Young, 1964].
A possible intermediate might be a Latin 4th-declension verbal noun *fūtus, with possible meanings including "act of (pro)creating".
From fūtuere came French foutre, Catalan fotre, Italian fottere, Romanian futere, vulgar peninsular Spanish joder, Portuguese foder, and the obscure English equivalent to futter, coined by Richard Francis Burton.
However, there is no clear past lineage or derivation for the Latin word.
In the Middle English of this poem, the term wife was still used generically for "woman".