Looking for a Red - looking for a specific one that someone may have used in the past that worked - French, Italian, Australian. Does one work better than the other.
Have used Rioja and Beaujolais a few times. It really is a toss up. Burgundy works. Coq au vin is a simple dish that should not be over analysed. In olden days the wine was added to tenderise. I always cook the porcini or chantrelle separate in a little bacon fat. Yummy
If you are hoping to get a budget(ish) bottle I think you'd be better off going new world with your wine - Chile or Australia maybe. IME, a cheap new world wine is much better than a cheap old world.
I would have thought Beaujolais would be too light anyway but maybe that's just me.
I would agree with Chocks Away and Strathespey. As long as the wine is something you'd be happy to drink yourself it should be fine. I've often made coq au vin and just slosh in whatever I'm planning to have with the meal. I've never had any complaints!