wikiwand.com/en/List_of_countries_by_suicide_rate:
(suicide rates per 100,000 population, 2019)South Korea 21.2
United States 14.5
Japan 12.2
Switzerland 9.8
France 9.7
Czech Republic 9.5
Germany 8.3
Denmark 7.6
I don't think, Switzerland has a high suicide-rate. Can you link your source? What you've perhaps read: A high suicide-rate with guns in Switzerland. But over-all similar to other western European countries, I would say. In countries with less guns, people use other means to commit suicide.
I included Czech Republic in the list because they have the most libertarian firearms law in the EU (as far as I know). France gun law is similar to Germany's (mediocre).