Are language courses (German, French) tax deductable? If yes, does it need to be "approved" by the employer that it is needed in job?

It will probably depend on your canton, but I doubt the employer has to approve it - the tax return is between you and your Gemeinde.

I deduct mine in canton SG with no problems.

It doesn‘t do any harm to claim for it - there‘s no penalty for reasonable items that aren‘t quite correct, they‘ll just remove it if necessary.

I also deducted language courses without problems.

Just add it in and see if they accept it. Unless your employer paid for it, then no

In my case another canton paid for it .

Just wondering for next year: Did you submit proofs/ receipts for your language courses? I take classes with a private teacher (paying her through bank transfer every month), how should I deduct these fees? And are only courses for national languages of Switzerland (i.e. French, German, Italian) eligible?

You will need receipts; the private teacher should provide them.

Even if you paid for the course yourself, I would advise to get an confirmation in writing from your employer that improving the language skills is beneficial to your employment situation, if they are willing to do it.