Well, you've got an odd situation on your hands. I suppose it matters whether this is in 1940 (as a means to bypass the Maginot Line) or something like 1941-2.
The Swiss are immediately going to join the Allies. But Unless a friendly France is on their border, there is nothing that can be done. The Swiss are going to collapse.
The odd result is that the Swiss Nazis might play a critical role in the situation. Undoubtedly, if the Swiss were a target, Hitler would try to crack the government as much as possible. This could follow the Austria, Czechoslovakia and Poland model--force the Swiss into concessions, and then deal a killing blow. Certainly, he has no need to blitz into Switzerland, as they are already prepared anyhow, and this might make it much easier to take down.
The role that Franz Burri plays in Switzerland is going to be critical to determine whether Switzerland becomes a Denmark or a Netherlands. It should be bad, but the Swiss Nazis might be numerous enough to make a difference.