Sprinkle the cavity with 1 teaspoon of the tarragon, Cut 1 lemon in half and place a lemon half in cavity.
Squeeze the remaining lemons; you should have about ¼ cup juice. Melt the butter in a small pan over medium heat. Stir in the lemon juice, the remaining 1 teaspoon tarragon and the mustard; mix well. Brush some of the butter mixture over the surface of the chicken. Place breast-side up in a shallow roasting pan. Arrange the onions around the chicken: brush half of the remaining butter mixture over the onions. Roast in the oven for 30 minutes.
Spoon the vinegar over the onions and stir the stock into the pan. Baste the chicken with the pan juices and roast for another 30 minutes. Baste with the remaining butter mixture and season with salt and pepper. Continue to roast until the chicken is tender and golden, another 20-30 minutes.
Make a bed of watercress on a warmed platter. Place the bird on top and surround with the onions. Baste the chicken with some of the pan juices and serve the remaining juices on the side.