Well for one, my ancestors would become Americans much sooner.
But more seriously, the new republic is going to have a lot of figuring to do.
Maine doesn't exist yet, it is all part of Massachusetts & Vermont doesn't actual join the union for several more years. So, it is quite possible that American Lower Canadia enters as it's own state or as a part of Massachusetts or New York.
However regardless, this is going to cause a major issue. Lower Canadia is full of French speaking "papists." Not a group many Americans are going to be happy about having the ability to participate in elections.
Lower Canada is also still under the semi-feudal seigneurie system. I can't see American politicians leaving that in place.
For elections, I could easily see something like English literacy tests as being a requirement. This would be a simple way of disenfranchising the "undesirable" population.
Removal of the seigneuries is going to ba a top priority of the governors & any local anglophone administrators. The problem is I doubt they'd have a sufficient plan thought up to do so. Leaving most Lower Canadians destitute before, most likely settling, into a sharecropping system with anglophone landlords (perhaps absentee landlords to boot) instead of the seigneurs.
You may actually see public schools take off earlier in these areas. But they're goal wouldn't be to provide a base level of education. It would be to anglicize & protestantize the locals.
I don't see this as that likely on it's own though. It certainly isn't ASB, but the northern "Maine" border was left undefined for over half a century after the Treaty of Paris in OTL. So, I don't see it being enough of a priority unless something else changes.
Perhaps, the Canadian expedition goes a bit better, but still fails to take Québec. That way the Continent Army technically occupies the area already. That shouldn't change anything I said either.