If I'm a paramedic in New York and I want to move to Montreal, how would I go about getting a job as a paramedic there?

Why not get in touch with the Canadian consulate in your area? Or you can google 'moving to Canada.' Or ask this in the Canada forum.

1) How is your French? The language of business for government services in Quebec is French. You need to be fluent including medical terminology. 2) Paramedic training and certification in Quebec is its own beast. I have no idea how your training will transfer over to "Le Belle Province." Getting a Primary Care Paramedic license in Ontario might be a little easier.

You don't have top give up your citizenship if you marry your GF, as suggested by another answer. However, you need a work visa unless you qualify for a TN status job: http://en.wikipedia.org/wiki/TN_status Best is for your GF to check with Canadian Immigration about options for you.

If she is a Canadian citizen and you're willing to give up your US citizenship, you could marry her, which (to the best of my understanding) would entitle you to apply for Canadian citizenship. Upon become a Canadian citizen, you would be eligible to be considered for any job in Montreal. (Of course, it would be of very great help if you spoke fluent French, since government activities in Montreal are bi-lingual, with an emphasis on French.) For a simple move, you're talking about a number of major decision points. Think carefully and do research.