I realized last night during a work discussion around beers that after 5 years on my job, a part of which entails me dealing with a wide range of the public, on the phone or in person, I have only had one person give me shit about not being a true francophone or not speaking french correctly and he was already in a rage about our organization and our phone system (and rightly so on the latter). Quebec is, very broadly speaking, still an insular society and often reverts to a self-defeating defensive stance, but the people are fundamentally generous and accepting. My french can be rough at times and I have to talk about a crazy range of things with some of the calls I respond to (geothermal, cats stuck in trees, taxes, government databases, real estate to name just a few from the last couple weeks). People are always very patient when I am lacking a vocabulary word. Sometimes I can even hear them trying to make me feel like there is nothing wrong with my french, when I know that I have just said something completely incomprehensible. The worst that has ever happened is that sometimes people switch to english, but strangely, this is very rare over the phone. Maybe there are some visual cues that help people determine what your native tongue is?
In any case, if you feel insecure or worried that people are going to laugh at you or be offended when you try and speak french here in Quebec, push those worries aside, go forth and speak your mind. When you slip, the francophones will be ready to grab you and make sure you don't fall.