Some people say only thin lines separate poetry, prophecy, and madness. We don't know if that's generally true, but it is in the case of vatic. The adjective derives directly from the Latin word vates, meaning "seer" or "prophet." But that Latin root is, in turn, distantly related to the Old English wōth, meaning "poetry," the Old High German wuot, meaning "madness," and the Old Irish fáith, meaning both "seer" and "poet."
Latin vātēs, vātis "prophet, seer" (akin to Gaulish—Greek spelling—ouā́ teis "those performing sacred rites," Old Irish fáith "seer, prophet," fáth "prophecy, prophetic wisdom," Welsh gwawd "song of praise, satire"; Gothic wods "possessed," Old English wōd "raging, senseless," Old Norse óðr "frantic, furious," all going back to Germanic *wōd-; Old High German wuot "rage, frenzy," going back to Germanic *wōdi-; Old English wōth "sound, noise, voice, song," Old Norse óðr "mind, sense, song, poetry," both going back to Germanic *wōþa-) + -ic entry 1