The problem is that Marx's labour theory of value predicts that it would not be possible and not even desirable.
The reason Champagne is expensive is that the traditional method of making it is very labour-intensive, especially the remuage process where each bottle is turned a minute amount by hand and le dosage where wine and sugar are added for secondary fermentation.
Under a socialist system, wasting precious man-hours on such a decadent and frivolous product, when the manpower could be used to produce essential goods, would be total anathema.
If you want Champaign for everyone, you need a capitalist system where large amounts of capital is invested to automate the process, which would lower the price, and make it accessible to all.
Reading that back this image kept popping into my head