I adore the second part of Amy Grant's rendition of "Jesu, Joy Of Man's Desiring": https://youtu.be/Qun3aiwcxB4?t=1m45s
I'd love to find more music like this but have no idea how to describe it. I'm not great at picking out instruments but it sounds like there are some traditional instruments (fiddles, pipes/flutes, and is that a bagpipe?!) with a full orchestra behind them.
The best I can come up with is "jig backed by an orchestra" but am hoping that you have better terms or can point me to other songs/artists in this style.