Most of the time when people say "fiddle tune", they are referring to a piece with a fast tempo and short notes. Lots of eighth notes, a handful of sixteenths (probably as pick-up notes) and few notes which are any longer. The few longer notes will probably come at the end of sections.

If you don't believe me, take a look at the Fiddler's Fake Book, which could have been titled "50,000 Eighth Notes."

If you pick up a fiddle and play something slow, such as "Danny Boy," then it's not referred to as a fiddle tune, it's called an air.