A commentor has pointed out that the usual Latin reflex of P.I.E. *gʰ is not 'f', so I will put my response to that commentor here:

I got the connection from the IEW, which is outdated nowadays, but I maintain fūtis is more likely to be a reflex of *ǵʰew than of anything else. Most I.E. descendents of *ǵʰew (the majority of which are uncontroversial as far as I know) mean something like 'to pour,' and the Latin reflex means 'jug,' with the adjectival form meaning 'leaky.' While P.I.E. *gʰ does not typically go to f in Latin, P.I.E. *gʷʰ does, and the difference is only in secondary articulation. Interdialectal borrowings account for far bigger exceptions to sound laws; considering how similar *gʰ and *gʷʰ are in articulation, I think it can account for this one, especially since the meaning of the Latin reflex and the apparent meaning of the P.I.E. root are so similar.

The fact that the English word 'God' is cognate with several IndoEuropean words meaning 'to pour' is unaffected by whether the Latin word is a reflex of the I.E. root, but I think it's fairly clear that it is. If there have been any better suggestions as to the origin of fūtis, let me know and I will amend this.

Thank you to the commentor for pointing this out, either way,