Interesting remark. Fairs and Markets overlap in function. Sometimes we talk of trade fairs, and of course what I call a market is where I buy food.
I may be wrong but the Danish meaning invoked a traitional idea of market and fair together as would have occured in the UK in previous centuries and i suppose still occurs a little in the form of a village fete. So I used the word 'fayre' as it seemed closest to the traditional Danish meaning. Computer said no (Not surprising as it isn't in every dictionary, but nethertheless we are interested in languages here arent we?).