Funny to see College Platon mentioned. It was right around the corner from my first place here and my roommate told me about the huge scandal.
Doing a quick
search I see some programs pop up that will do courses for just a week (like Sprachcaffe or Sainte Anne) though I couldn't speak to the quality of any of them. I don't love giving traffic to MTL Blog but they have a
list of some programs and some of them do just one week. Somewhat ironically it might help if you search in French for
séjour(s) linguistique(s) (some of the free language courses for newly-arrived immigrants are advertised on public transportation...in French). The institutions I recognize as being reputable, such as the various universities and the YMCA, don't seem to have anything for just a week. Though the YMCA has
private classes available which you may be a good option - the value of Canadian dollar vs. your home currency can make it an affordable option and you can do fewer hours with more results being one-on-one.
You can also check out language exchange groups such as
Mundo Lingo which has several conversation nights a week as well as the many, many French Meetup groups/events (explicit language exchange ones as well as social meetups in French).
Also, instead of or in addition to classes for learning French you can also take a bunch of other classes that just happen to be in French such as cooking classes, fitness/dance classes, music classes, go to a board game cafe, go on walking tours in French, check out films or live theater, check out AirBnb "experiences" (various tours/classes/workshops) for stuff in French, etc. Another thing to consider - summer is festival season so there may be opportunities to volunteer while you're here to get a lot of experience talking to the public in French (such as
Juste Pour Rire during the end of July). If you need any help finding cool stuff or cool events to enhance your French experience let me know and I can suggest some more specific things for you.
If you don't already have lodging set up I'd just say your best bet is to stay in neighborhoods that aren't around Downtown (especially around Concordia and McGill) since they'll be a lot more Anglo, especially with summer events bringing a lot of people from out of town into the city.