Did anyone notice the 'Bagad' band playing in the OP parade video? 

The Bagad bands traditionally include Bombards, an oboe-type woodwind (basically a chanter?).  There's also a tradition in Brittany for dances to be accompanied by a duo - usually (but NOT always) a Bombard player & a Bagpiper... see where I'm going with this?  A FIDDLE would be a PERFECT replacement for a bombard - there's some very interesting Breton 'Bagad' music to play! 

BZH New York [Association of Bretons in NY] is proud to welcome Bagad Bro Dreger, a traditional Breton band from Perros-Guirec, Côtes-d'Armor, a picturesque seaside town in Brittany, France. This will mark a rare and thrilling opportunity for New Yorkers to experience the powerful sound of bombards, binious (Breton bagpipes), and drums as performed by a 48-member ensemble.

Here's a better view at a different point in the parade.

Here's a performance by Bagad Sonerien Bro Dreger from last year. 

I probably should've mentioned... not asking anyone to help me with the names of any Breton music! 😄 

Brittany does have some interesting trad rhythms, and I do understand wanting to reclaim cultural ties to earlier instruments, but I am prejudiced & think ALL music sounds GREAT played on the fiddle. 🤗 

...in the meantime, with all the tune comparisons I did, I now have that little tune from the parade credits firmly planted in my memory, as 'St. Patrick's Parade' (for now)!