As fermentation is a biological process it must need to occur in the cellular environment.
Where does fermentation occur?
Fermentation occurs in the cytoplasm of both eukaryotic cells and prokaryotic cells.
Fermentation takes place in the cytoplasm of prokaryotic cells like bacteria. Not only fermentation, but all kind of metabolic process also occur in the cytoplasm of prokaryotic cells.
Fermentation also takes place in cytoplasm of eukaryotic cells like human, plants and fungi. It occurs in the cytosol of cytoplasm, which is a fluid part of the cytoplasm.