Last time I checked for my other half she doesn't need a visa (as a 3rd country person would do) but has to register at the Prefecture for stays >90 days. The other stuff is straight from the FR system (and I've just done it again for a German and it gives the same answer!). However it doesn't avoid the fact that Ireland is not in Schengen so Irish people travelling inside Schengen areas are subject to different rules than those domiciled inside Schengen. It's confusing and even the Irish websites give conflicting/confusing info.
repeating myself, the form does not apply to EU citizens so you will not get accurate results for Germans or Greeks etc