If you're planning on living in Switzerland, then you'll want to be fluent in either French or German (preferably both,) depending upon location, so there's still time to learn. If you're working for an international firm, then they probably hired you, an American, for your common law background, and you'd be working on such cases whether you're in Geneva, Switzerland, or Geneva, New York.
If you want to actually practice Swiss law, you could go to university and get another degree (equivalent of a BA, as law is taught as an undergraduate "major" in Switzerland.) Or you could apprentice with a local firm for a couple of years.