If you are interested in taking French language and culture courses, I would recommend taking part in an intensive language course- most, if not all, programs will find a host family for you. I did the same thing five years ago, although I did not stay with a host family...I studied Spanish language in Spain for two months, and had the option of staying with a family, though I chose to live with students instead.

Here is a program I found in Montreal, which offers language courses, usually between fours weeks to several months.

http://www.learnfrench.ca/french-language-program-courses.aspx

...at the top of the website, you can click on the link, "homestay," to get more information on that.
I'm not sure if you can stay with a family for such a short period of time.. you could do an "au pair," where you are hired to babysit children in exchange for housing, but that usually requires a long term commitment (around one year). I'm not sure about options of staying with a host family for less than one or two months...
but if you are interested in taking language and culture courses (which I highly recommend), there are plenty of programs. You can google, "French language programs, Quebec," and you'll get a lot of results. Montreal is a beautiful city, with lots to do, but if you'd like, there are also other places in Quebec you can study in.
Hope I helped!

Thanks for all the effort you put into your answer, lots of good info! Thanks for writing =]

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