Hi,
You will be eligible for OFF campus work permit after 6 months of full time studies, ONLY if the educational institute where you are studying, is participating in Off campus work permit programme. Any other educational institute NOT on the list, will automatically make you ineligible to apply for Off campus work permit.
Here's the list:
As you can see, most of educational institutes are French medium, and the only English medium educational institutes based in Montreal are - McGill Univ., Concordia Univ., Dawson College, HEC Montreal (offering Management programmes in English medium) and Marianopolis College (in Westmount).
As for part time jobs, it really means where you work/live and your contacts. There are anglophone people in Montreal/GMA, who do not speak a word of French, and yet live in Anglo dominated areas such as West Island. You may find jobs with employers from Anglo community or even your own desi community, but you need to know people, and make contacts. Go out and search for jobs.
But, yeah..in overall sense, most Quebec based jobs (especially entry level and/or which requires interaction with customers/clients) demand that the applicant is Bilingual (i.e speak both French and English), and in my personal opinion one should know French, when living in Quebec, not just to have greater leverage in finding employment, but also to actually immerse in Quebec culture. Unless, one is pursuing highly technical M.S/PHD in engineering/sciences/research in University etc. .... in most cases knowing French will be highly beneficial. It is strongly reccomend for anyone going to Quebec, to learn atleast lower level intermediate /DELF B1 level French( if possible higher intermediate level B2) so as to somehow manage to communicate and gradually pick up French fully by staying there and communicating with locals in everyday life. Saying this, it does not mean, that one cannot get job without French..as ultimately it all comes down to who you know, your talent, where you live and of course luck.
Hope it's clear.
Best of Luck.