I was going to post an intro for my first post, but I saw this question and couldn't resist.
Ask your school. They should have a department, or at least a person that deals with externships. Find out if anyone's gone overseas and how they got there. Find out what the rules are for the school, the paperwork involved, anything the employer has to do. If you can streamline things for the employer, they'll be more likely to hire you.
How long is your internship for, and even more important, how long do you want to be abroad? If you're willing to stay a full year or more, that will increase the likelyhood (isn't that a word?) of someone taking you on. Make yourself a good investment for them, someone worth the trouble of whatever red tape they'll have to go through to hire you.
From what you want to learn, I can recommend Austria. The pastries there are wonderful (think Vienna) and the bread is well made. The only thing though is that pastry shops and bread bakeries are two different animals in that country. A baker is not usually a pastry chef and vice versa; you may have to choose, especially if you're there for only a short time. This is a normal thing in continental Europe.
Whatever country you want to go to, try and speak the language. Yeah, everyone speaks English, except when they don't. You don't want to be the only one that doesn't speak the native language, it'll make you nervous and make trips to the countryside harder. Besides, it makes you look good.
If your school can't help you and you have to go it alone, I can recommend a good agency that can get you a training and work experience visa for the UK. Don't laugh, they're doing good things with food these days. :)
Alternatively, take a good look at your heritage. Some European countries do things like ancestor visas which is if your family is a fairly recent arrival to America (grandparents or less) then you might qualify. Look into EU regulations and the regulations of individual countries for more info.
No matter what you do, it will not be cheap. Not only are the visas and permits expensive, but both the Euro and the Pound are doing quite a number on the dollar right now so making your way over there will be costly.
If you can get something through your school, that's probably your best bet at this stage, but if you can't, wait until you graduate, work a bit, get some experience and some money and then get your butt over there. It can be done. Good luck!