First, the mountain biking. I'm also into the cross-country & single track stuff. Unfortunately I've been pretty disappointed with what I've found here, you can read my rant about it in this post.

More specifically, the cross-country riding around here isn't great - the Alps are generally just too steep for it., and when it is not too steep they put a paved road in instead of a trail. So, be prepared for some super steep climbing then some serious downhilling, but not much in between.

The Jura mountains are a little better, and are just as close to Lausanne as the Alps. However, there doesn't appear to be much of a trail network there, and the few good trails that are there, you need a local expert with you to enable you to know about them.

Everything that I've seen and heard about the riding near Zurich sounds like it is better than here. Yes, the mountain there aren't as big as in Lausanne - but that is not a bad thing. There also seems to be a larger mountain biking community there. So, for the mountain biking then I'd go there.

As for the language, in Lausanne it is nearly all French. The next most common language that you hear on the streets is Portuguese, followed by English or German. The German is a mixture, most of the German-speaking people that I know here come from Germany, and so speak high-German. There are some Swiss-German people here, but not as many as you would expect. Anyway, I don't expect that you'd learn much German by coming here unless you enrolled in a specific course, in which (fortunately) you would learn high-German and not swiss-German.