As I recall, poule au pot is just a poached chicken, usually an old, tough stewing hen. Throw it in a pot, cover with beef broth, toss in some carrots, a leek or two and, uh, some root vegetable. It might be parsnips or turnips, I don't think it is potatoes in the traditional recipe. Bring to a low simmer, cook until the chicken is done, maybe 45 minutes or so. Tarragon and a wee bit of rosemary might be a good bouquet garni. I think the use of beef broth to poach the chicken is based on the idea that every French country farmhouse has a big cauldron of pot au feu going at all times. If I were doing it I'd probably throw in a bay leaf, a clove and some chunks of garlic as well.
I might have a real recipe for it in one of my books, I'll try to remember to look for it in the morning.
mjb.