Without being aware of your exact immigration status, it would be difficult to determine whether or not you qualify for local tuition. I did do some research online though and found proof that you are exempt from international fees for CEGEP and university with your selection certificate, but could not find anything about secondary school.
I also found this news article that talks about private versus public schools:
https://www.cbc.ca/radio/sunday/the-sunday-edition-october-29-2017-1.4374949/are-quebec-s-private-high-schools-creating-a-segregated-society-1.4374965
One in three Quebec students go to private secondary schools partly thanks to generous subsidies from the government. At the end of the day, it is your money and you have the right to use it as you see fit. All the French private schools are pretty much 5k a year if you can get the local rate. If you would like a list of the cheapest non-subsidized private English schools, let me know and I will do some research for you. I am sure I can find many that are way lower than the 25k mentioned by Canuck.