I learned this tune from a recording by the Quebec group Ni Sarpe Ni Branche, with fiddlers Claude Methe and Simon Riopel. I love the way that the second part effectively borrows 2 quarter notes from the first part. Try this one out on your favorite accompanist. "Ti-Douard" is a colloquial shortening of the name "Little Edward," though I don’t know which particular Edouard the tune is from/for.
Probably named after:
Edouard Richard, fiddler….likes crooked versions of familiar tunes.