'She Moved Through the Fair' was based on a traditional song (see numerous discussions here on the subject; the name of the writer isn't in doubt), but it wasn't in Gaelic. Probably the Gaelic text mentioned is a modern translation into that language, or a song on a similar topic. The 20th century rewrite is a feature more of the revival than the tradition, having been popularised via a commercial recording by 'Count' John McCormack and later by Margaret Barry.

For interesting background on 'Pretty Saro' (a late C19 American development of an Irish song) see also past discussions here, all of which can be found via the search engine.