lol, now that one does take the cake. I've seen lots of odd names before, but this one appears to have been written phonetically by the priest according to his understanding of it. Neither godparent could sign, the baptism says the father was absent.
The other children I find for those parents are named:
from baptisms: Marie Thècle, Firmin, Marie Henriette Célina, Marie Philomène Arthémise, Michel, François Xavier, and from marriages: Emma, Claire, Pierre. There may be more.
She actually could sign and wrote Marie Épousitienne Gagné on her marriage, her sister signing Marie Arthémise Gagné.
I think from looking at these names that the parents were trying to get unusual names for their children, probably to differentiate from all the other Gagné children around, that family name is quite common.
Frankly I think they invented the name, possibly combining forms to arrive at it. You'll probably get a database error on the thing as unusual name, just mark it false error.