Aren't Swiss firearms heavily regulated? Such as registration, ID's when purchasing ammunition and required licensing? They are also very well educated on firearm safety thanks to those regulations. The only thing I wouldn't care to see implemented here is mandatory firearm registration.
Edit: Yeah, not the typical gun nuts idea of a paradise at all...
https://en.wikipedia.org/wiki/Gun_politics_in_Switzerland
The regulation are not too different than what is usual in Europe, however as you can see in the article hunting rifles & hand bolt rifles (for example a K31 rifle) can be bought without a permit, merely a simple declaration. That would already cover a lot of ground as far as common firearms go. Swiss gun stores are usually well stocked. That it is considered an haven is probably projection from outsiders but the fact remains that there's a lot of guns in Switzerland per capita (although less than in the US). AFAIK in France you can buy some guns (22lr and single shot hunting rifles) with a simple declaration
provided you have either a sport or hunting licence.
All that being said, Switzerland obviously a vastly different gun culture than the USA or even European countries. Thus we come back to the original point : the US problem is first and foremost the gun culture. The large amount of firearms available are "merely" an aggravating factor.
EDIT : On gun related deaths, the number is often deceiving IMHO, as it counts suicides by firearms which are more prevalent with higher ownership. Suicides are a bit zero sum, with no guns people find other ways to off themselves. What separates the US from the rest of the first world is the frequency of gun homicides and mass shootings.