Hi Nikolaj,
Thank you for sharing the page.
I do see why this might be a concern and if I were doing this, I would change the text at the top first - 11 occurrences in this small text area is far too much and will be seen by Google as such.
Then there are the listings, and this is where it gets a little more tricky because I don't believe you need to remove everything here - but I would do something with each Champagne title. If I take that first bottle as an example:
Champagne - Brut Origine - Halve
There is no need to have Champagne here - go to the page for that bottle and it doesn't say this. It would be much easier to read if you remove Champagne from each of these headings as the word just gets in the way - you already know you are looking at Champagne, so no need to keep putting it.
Then you have:
Fra Champagne Henri Mondi - again, there is no need to have Champagne here because it is just Henri Mondis, not Champagne Henri Mondi.
Do this with each listing and your page will be much healthier, have a lower word count and with that, much less keyword stuffing.
You were absolutely right to check on this.
-Andy