Shyness apart, if you feel nervous when speaking French, it's probably due to a lack of confidence in your skills: you don't feel you have the grammar, vocabulary, and/or pronunciation needed in order to express yourself. The obvious solution is to improve your French, and this site is filled with resources to help you do just that. Beyond lessons and learning, however, there are other ways to increase your confidence and feel more comfortable speaking French.
We All Make Mistakes
First of all, you should know that most people are forgiving of mistakes in their native language.* Think about it - when a non-native speaker addresses you in English, are you really thinking "what a dummy, his sentence is all out of order, and that's the wrong verb, and the less said about his pronunciation the better"? Or do you try to meet him halfway, ignoring or perhaps mentally correcting mistakes in order to understand what he is working so hard to say? For most of us, it's the latter, because we appreciate the effort people make to communicate. In my experience, the French much prefer that you speak to them in broken French, rather than being asked to speak to you in broken English - because they're just as anxious about their English! So don't let fear of how you speak French stop you.
If you're going to ask a question or buy a train ticket, think about what you want to say and how to say it before your turn comes. Try to anticipate what questions you might be asked and what additional information might be needed.
Talk About Yourself
Whether you're interested in current events, wine, or traveling around Alsace, read about those topics and make a list of the words and phrases that crop up repeatedly. And if you find that you're regularly getting pulled into discussions about tennis or movies, try to learn some of that vocabulary too.
Practice Every Chance You Get
Speaking French is like playing the piano or making bread - the more you do it, the more comfortable it feels and the easier it gets. Join the Alliance française, take a class, or place a classified ad to find someone to chat with regularly, even if s/he isn't fluent or native, but just another nervous French speaker like you. Even introverts can make friends - and have to if you are serious about improving your French. As you practice, you'll gradually feel more comfortable and confident.
Just Do It
Finally, just try to relax, have fun, and remember why you're learning French in the first place. It's all about communication, so get out there and speak!