If you're desperate and don't mind a bit of a drive, you can always consider other towns outside of Fort Kent like Madawska, or even Caribou. Caribou is a little far, but it's a bit bigger so you may have more options. And definitely speak with realtors, because many know people who rent houses but don't advertise, or they act as property managers for different rental properties.
As far as Craigslist goes, I doubt that it will be of much help. Any time I've ever looked, it's mostly focused on the southern part of the state.
It can be difficult to find housing that accepts pets. Everybody has dogs here, so you'd think they're would be more options. In the past I've spoken with people who will reconsider their pet policy if you ask. Many will consider dogs, but seldom cats.
Also, I would definitely check out the different local paper(s) online. For example, here's a link for the Fiddlehead Focus rentals:
FiddleHead Focus | Classifieds | Classifieds | Rentals
Fort Kent is rural and somewhat isolated, so you need to be a bit resourceful!