It is possible to protest about both.
Champagne and fromage is neatly symbolic. It may not be, per se, particularly worse than any of the other "mid-range luxury" establishments colonising the village, but there is a symbolism to champagne as the ultimate libation of the rich, which makes the inequality and contrast impossible to ignore for lots of people. Then the word "fromage" seems a bit pretentious, because it's French and we've a perfectly good English word for it (and easily as good british cheeses, for that matter)... The pretentiousness invites attention and then contempt, and galvanises people to protest.
I like cheese and fizzy wine, but I totally get why these guys are fair target.