Another possibility (although it's technically still in North America) would be St. Pierre and Miquelon - a French overseas territory just off the coast of Newfoundland. You can fly to St. John's on AC and then rent a car or take a local taxi/ferry. It's an absurdly remote place that no one's ever heard of, it's tiny and quiet and you can totally relax and unplug, and it's a French-speaking environment, complete with the food and culture. The ocean scenery is stunning, and from what I gather you can do a bunch of hiking/boat excursions and the like.

I've never actually been, but last fall I did spend a few days in Newfoundland very close to where the ferry to St. Pierre leaves. I stayed at a gorgeous B&B in the town of Grand Bank and have never slept better in my entire life.