Cock-a-doodle stew.Photo: Courtesy of Paris CommuneCoq au vin is no rarity on New York menus, but, then again, what New Yorkers usually get is not really coq au vin: It’s just chicken braised in wine. The gamey, bold flavor of a sinewy old rooster, its tough flesh turned velvety by twenty hours or more of braising, is a different thing entirely and one of the summits of French cooking. For a few days, anyway, you can get it at Paris Commune. The restaurant, which has a rooster as its symbol, has gotten some old birds and added them to the menu tonight and through the weekend as a $22 special, with the traditional accompaniment of bacon, pearl onion, button mushrooms, and baby carrots steeped in Burgundy and brandy. As with any true coq au vin, the real draw is the intense broth, which is to standard chicken broth what George Clooney is to Chad Michael Murray.