Somewhat ironically, Switzerland has four official languages, none of which are English, but with so many regional dialects within those, English is quickly becoming the… ahem… Lingua Franca:
You'd get by just fine. It's not uncommon to speak three languages fluently in CH (given it has 4 official languages), and usually English is in the mix. I lived there for a couple of years and while not speaking French or Italian, I got by quite easily in the respective regions.
Get by, yes its often enough. Job search - that limits your choices maybe to 10%, in a job market that is consistently overcrowded (100-500 applicants for any good position, not all are brilliant and with right experience but some always are, whole world tries to get here).
You will regularly hit the language wall in places like shops, post office, neighbors etc. where answer in given language if they speak english is consistently "no". Integration outside big cities is a lot about you becoming like them, not vice versa, better keep the differences compared to locals behind doors of your home. Smaller cities, more rural places - forget english outside tourism, many young speak it but otherwise there isn't much will and often neither skill. French part is worse than German part in this (just like French from France are much, much worse when it comes to will to speak english than Germans from Germany are).
https://en.wikipedia.org/wiki/Languages_of_Switzerland#Engli...