Do you have to stay in Vevey? Because if you choose to learn German, I would recommend moving to a German speaking part of Switzerland, and then attending a basic German class there, because as stated above, to participate in German classes in Vaud you need to speak French.
If you have money to spend and time to lose, you could join an intensive course in language schools like ESL, but again that would mean moving.
I recently had to train my German for an interview and I use Strokes easy learning software. I bought it in Manor I think but you can find it on amazon.
I thought it was very good, it goes from easy to business level and it helps you work on grammar, vocabulary and also your pronunciation if you plug in a microphone.