True, although if you come to Quebec on a work permit, you are eligible for English schools (my kids went there for almost two years now). However, they state that once you are a PR you have to send them to French public school.
Though there is another law that once your kid studied at English school for at least a year, they might be able to continue. I haven't tested this last part since we are already moving out of QC.
Another option is to choose Semi private schools instead of full private. The cost difference is almost one 4th. A full private might cost around 20k per annum per kid vs 5k for a semi private.