Switzerland is now officially part of Schengen, so you should have no problem entering it if you possess a Schengen visa. That they haven't implemented the treaty at the airports does not influence that fact that they no longer issue 'their own' visas. What it also means is that some US green card holders who didn't use to need a visa for Switzerland now do.

Also, you can exit GVA to France, as the airport in essence straddles the border. You have a valid Schengen visa, so you could take a French cab into France, then across a land border into downtown Geneva.