I will comment on French speakers because the bulk of francophones in Quebec, particularly in Montreal, want to learn English.
The problem arises in high school, where English instruction does not seem to be adequate for a certain number of francophones. That is probably one of the reasons why, in the era of globalization, some francophones wish to continue their education in English and become more proficient in English. In Quebec's case, the answer is to enhance the English courses offered in high school.
Nevertheless, that poses a challenge, because as soon as people have better English skills, they have better access to CEGEPs.
It's a complicated issue, but there is another solution, one that the CEGEPs, themselves, would probably have to implement. It requires CEGEPs to strike a better balance in the education they offer in both languages, including for English speakers in Quebec interested in learning French and becoming fluent.