Rohirric and Elvish Verse

[HerenIstarion]

It seems explainable on the following ground:

Faramir to Sam and Frodo:

Indeed it is said by our lore-masters that they [Rohirrim] have from of old this affinity with us that they are come from those same Three Houses of Men as were the Númenoreans in their beginning not from Hador the Goldenhaired, the Elf-friend, maybe, yet from such of his sons and people as went not over Sea into the West, refusing the call.

Thus, as the poetry of Three Houses must have been largely based on what they've learnt in Beleriand from elves, similarity is natural.