Can I say from experience that there is nothing?/much? it’s vegan. But, I suspect there are vegetarian options. (I haven’t been to a Swiss Chalet in years, for this exact reason… although my husband loves it)
Here is its nutritional information: http://swisschalet.com/mobile/nutrition.php
Looks like salads, maybe fries or mashed potatoes, veggie burger, desserts…. Most soups are probably not vegetarian, in my experience. (Delicatessens and Mediterranean/Persian restaurants tend to have a daily vegan soup… usually lentils. But most other restaurants use chicken or beef broth… even for their vegetable soups. You have to ask.)