It is very possible to get by in Montreal without speaking French, but being a strict anglophone has its limitations. Learning French is not only a good way to exercise your brain, it's also a way to boost your confidence, so you can make your way around the city more easily, navigating grocery stores and restaurant menus, alike.
TL;DR Below you'll find places where you can learn French, either for free or for relatively cheap.
In Montreal, many anglophones have the unique opportunity of being immersed in another language. So, make the most of it and take some French classes! I've rounded up some great resources below for people who want to learn french for cheap.
The YMCA is probably best known for offering cheap membership and exercise classes. But little do you know, they also offer French classes. They have a wide variety of classes, all of which depend on your goals and your schedule. If you want to have an introduction to French, for example, a 7-week, 4-hours a week course will cost you $282.
The Language Laboratory at the BaNQ
At the beautiful BaNQ, on Berri and Maisoneuve, 2 workstations are reserved for patrons who have signed up for the Francisation en ligne (FEL) courses offered by the Québec Ministry of Immigration, Diversity and Inclusiveness. The courses are totally free. You can also access a wealth of other language-learning programs, like Rosetta Stone.
The Quebec government really encourages new immigrants to learn French (sometimes almost aggressively), and they have programs designed especially for people who are new to the province. The best part is that these programs are totally free!
These classes are aimed specifically at job seekers in Montreal. The four-week sessions assume that students have basic knowledge of French, and they will help you with CV and cover-letter writting skills. The classes cost $75.
Commission Scholaire de Montréal
The comission offers classes at various locations throughout the city. Classes run at about $75 per 8-week course.