It must be noted that the Algonquin month names aren’t entirely accurate. First, the word “Algonquin” was the word people downriver used to describe the folks in question, who refer to themselves as Anishnaabeg. There are a number of different names for the months depending on local traditions. The farmer almanac has been publishing these month names for some time, so they have gained in popularity.
There are plenty of other calendar systems used throughout Canada, however, I have found it difficult to find any reliable source of names and traditions. There is quite a bit written about the Mesoamerican calendars, but little about the native calendars of the northern parts of turtle island.