I am not in a same sex couple, but I was married in Quebec in 2010. You should get in touch with a notary (notaire in French) about the process. A public announcement needs to be made in the paper about 4 weeks prior to the marriage date. They will also handle getting the marriage license prepared. In addition they will walk you through choosing your marriage regime (basically you decide up-front how assets will be split according to a government approved method - there are 3 - prior to marriage, essentially a government written pre-nup), and if you like they can even be the officiant for your wedding ceremony (our notary was also the one who performed our marriage) or you can go to the courthouse for the ceremony (it's cheaper that way). Then they will register your marriage with the government, and in a few weeks you'll get your official marriage certificate. They will also keep original copies of your license, marriage contract and certificate in their vault so if there is ever an issue you can go back to them for it. Also, most notaries speak a decent amount of English so don't feel nervous if you don't speak much French.
You don't have to use a notary, but it really makes things easier if you don't know the system. It cost us about $1000 total, but the price was higher because we altered our marriage contract to make it specific to us and not just the general government language, and our notary came out on a Saturday night to do the ceremony.
I was visiting from the U.S. when I married my husband here (he's Canadian). There was no problem getting married here as a foreigner, I just had to show them my passport and an official copy of my birth certificate at the start of the process.
I really hope that helps. Good luck!
