I can't imagine it could be either. If Ringil survived the first age it would either be loot from Gondolin turned up from a hoard or possibly in the possession of Elrond or Elros via Idril or Gil-galad (accepting for this scenario the published version that he was Fingon's son). I can't see that an heirloom of Numenor ended up with a second son of the Steward. I suppose the hoard theory might be possible in the light of Glamdring but more likely might be that Faramir the scholar and benevolent to elves might have named his sword in honour of Fingolfin's. However I don't know of any textual reference to Ringil other than as Fingolfin's sword. So I suspect it is either movieverse randomly borrowing names or something seen in fanfic and wrongly taken as fact.
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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