According to my family lore, Lafrenière is derived from La Fresnière/lafresniere, Fresne being a tree (Ash). Although I've never actually heard anyone say this, fresnière could be the name of a place with alot of Ash, much like érablière has a lot of maples ("cabane à sucre"). I don't know what it's called in english, but I've heard the term "sugar bush". The place with a breakfast feast where everything is cooked in about 200 gallons of maple syrup. Yummy!, but I digress.
Anyways, we have Baron de La Fresnière. Since the 's' in lafresnière is silent, it would be easy for a clerk to leave it out when writing the name, like on a birth certificate for example. And of course, anyone who doesn't speak french would drop the accent (è), and you end up with lafreniere.
I'm gonna step out on a limb here, not being an expert on the subject, but alot of french canadian names, like Desaulniers, Desrosiers, Tremblay, Desormiers are similar from trees (Aulnes , Rosiers , Tremble / Poplar, Orme / Elm) and from what I've seen, these names only seem to appear once the French moved to Canada.But like I said, I'm no expert.
By the way, I'm trying to find my line, with little success. At one point, my grand-father (Marcel) did the tree, but I don't know what happened to it (that's where the ash-tree theory came from). My grandfather was Marcel Lafrenière, Married to Murielle Bond. His father was Joseph Lafrenière married to Hermine Plourde. Joseph Lafrenière was from Maskinongé. If anyone has this in their tree, I would greatly appreciate it.
PS: According to this same database, Nicolas Baron / Lupien's "job" in the colony was "domestique" (laborer I guess) for Antoine de La Fresnay, which is another possibility.