It's good idea to take classes throughout your dog's life - a reminder of the basics for you, and (assuming you find the right course) fun and stimulating for your dog.
In light of the Bundesrat's announcement yesterday re: obligatory courses for new dog owners, you'll probably want to find a course that is recognized by the BVET. Which courses are certified will be made public later.
There are many trainers out there, not all will be certified by the BVET.
Where in ZH are you, and how far would you travel? I could ask my trainer for a recommendation, if you like...
My dogs have done the basic obedience course, and those that are still relatively mobile and not away with the fairies most of the time

attend
Familienhund or special activity classes regularly. I find that ongoing training benefits me as much as it does my muttleys.
We do classes in German, simply because the trainer I like best only works in German. My German is functional, but far from fluent yet I've never had a problem with the course being held in German - just ask the trainer to demonstrate if you think you haven't understood a point. Also, while a trainer may only do group classes in German (or French or Italian), you might find that some are happy to do private lessons in English.
Unlike me, the mutts are all tri-lingual.

Seriously, I've worked with dogs who only 'spoke' Chinese, Spanish, French, Italian and German at the time I adopted them. I train my dogs in English as well as the predominant language of the area I live in. It's important that they know commands in English because, in a panic, I will tend to use English first. Understanding commands in the local language is important, as you never know when your dog will need to obey another person as well.
Dogs certainly understand more than one word for an action - Think of how quickly they learn every synonym for 'dinnertime'.

I start with the English command, then randomly change to German. They quickly learn that 'down' and 'Platz' both mean hit the floor - and that they will get a treat for doing as I ask.
After all, it's really about speaking 'Hundisch', isn't it?
ETA: Have you considered Clicker training? Or hand signals? I use both as well as spoken commands.
Two of my dogs are deaf, so I naturally need to use non-verbal communication with them. Once I started using hand signals with them, the hearing dogs quickly picked up on it and respond to hand signals as well as voice commands. The great thing is with signing you don't need to worry about which language is used. Also very useful when you need to 'shout' at your dog after Swiss quiet hours...

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Clicker training is a wonderful tool - the marker (the click) is a neutral, universal sound - no language issues there, either.