AmerK3,For many years, I worked with people from all over the world, including a bilingual woman from Quebec just about the time that I was taking a serious interest in learning French, so I've been on both sides of this predicament.
On the one hand, having to deal with someone at work who isn't proficient in your language is tedious and, quite possibly, very annoying. Some people seem to think that lousy pronunciation and bad grammar are no big deal as long as someone can figure out what you're saying, but this attitude is very naive and is only likely to work with someone with a profit motive.
However, this does not mean that your coworkers wouldn't be receptive to an honest effort on your part, as long as, it's in small doses. When I started asking questions about French at work, the woman was obviously reluctant to get roped into teaching some guy French. So, I would memorize small paragraphs, expressing my point of view on something, and while standing behind her so she wouldn't see me shaking in my boots, I would rattle it off. It was enough for me to have her say, “Hey, that's pretty good.”, without her even looking up.
Start with greetings, keep your encounters one-on-one, be very sure of your pronunciation, and don't expect a reply. Then drop it. Figure out who's likely to be receptive to your efforts and stick with them in one-on one situations. If it's working out, say a little bit more each time. You're just trying to get over the stage fright. Keep it brief and don't impose, except for something like, “est-ce la bonne façon de dire ça ?”. Then drop it. If all goes well, eventually someone's going to catch you off guard by speaking French to you and you just have to do your best to cope and not be afraid to pull your chute and politely say, “sorry, what does that mean?”, or better yet, “Pouvez-vous parler plus lentement ?” , so that, although you may have no hope of knowing what they said, at least they can see that you're trying. Any such encounters would give you something to slowly build on.
I think your situation, while not ideal, presents a great opportunity for you, if you approach it correctly.
Robert