There's indeed two programs, the College Program (which requires you to be studying something hospitality-related at uni) - that has a J-1 visa and you can indeed be placed everywhere. I think it was suspended for quite some time after 9/11, but it has ramped up again lately.
And then there's the "International Program", which gives you a Q-1 visa. With that, you're only allowed to work at your pavilion - plus, it probably isn't very compatible with your uni course-wise. From what I understand, the College Program actually gives you some course credits etc.
One of the problems with both is that they are quite long-term (with the International Program being for an entire year), but looking at what stepintothepink says, the International Program is a bit shorter - still, my uni would have never given me enough time, especially considering that I studied computing

Disneyland Paris is far less structured - their summer jobs are usually for three months or so, but they can be as short as one month (which is what I did) or much longer, depending on their needs. Good French is an absolute must, mine was borderline and really made life difficult - if it's too bad, you won't get past the interview stage.
Both have their merits - the plus-side of Disneyland Paris is that you get to learn French, and that there's no problem with taking the money back home, or any kind of visa shenanigans. At WDW, you're far more dependent on Disney (and I have seen plenty of people getting sent home over next to nothing), but the whole operation is organized better than in France...