M.85
I don't mean to dash your hopes with immigration but you are part right on what you have said and part wrong. It may be easy for you to apply to Quebec being a French National but as far as I know and remember (spent sometime with Canadian Immigration) you can not just pick up and leave, there is some sort of restriction that has been implemented to stop such things. For example, immigration to Canada, although federal, is handled to an extent provincially now - a way to attract immigrants to less populated parts of Canada and away from the likely hubs of Toronto, Montreal and Vancouver. There is a stipulation with this in that you must remain in the province for so many years.
On another point, although it says a few months, if you're lucky (which I hope you are) you are looking at the better part of 1-2 years. You are applying to immigrate and although you may meet all the requirements, points, etc. applications do not get approved solely on points, each case is evaluated and reviewed and I would be hesitant to say that it would be a walk in the park as your skill is not needed in Canada due to the lack of jobs and high numbers of unemployed pilots. You would be sadly seen as a burden to Canadian Labour. I guess the bottom line is that people would see it as why bring in qualified people to do a job in Canada while there are plenty of qualified and able Canadians willing to do it. As far as Quebec goes, they always do things a little different there but I think you will find similar hurdles.
Regardless, good luck. Just thought I would shed some first hand insight.