Verbier is in the Swiss French part of Switzerland. As a small country with 4 official languages (French, Swiss German, Italian, and Romansch), most Swiss learn at least a second language if not more.
While Germans would not necessarily understand the many Swiss German dialects, the French in the French part of Switzerland closely resembles the French in France.
The Swiss French rarely learn German beyond the secondary level; usually they choose to learn English. This means that English is widely understood and spoken in most tourist areas. You will not have a problem communicating if you don't speak French, but it is still nice to learn a few words.
If you are a French speaker, the most notable difference is the way the Swiss French count. They adopt a much simpler method. Instead of saying "soixante-dix," the Swiss say, "septante." Instead of, "quatre-vingts," it's huittante," and instead of "quatre-vingt-dix," it's "nonante."
Click here for some useful French for your holidays in the mountains.