Preheat oven to 400F.
Place the potatoes, fennel, carrots in a roasting pan in an even layer, drizzle with EVOO, season with salt and pepper.
In a bowl combine the soft butter, tarragon, garlic and a little salt and a generous amount of pepper. Clean bird and pat dry. With your fingers separate the chicken breast skin from the meat, working with about 3/4 of the total amount of the butter mixture, maneuver half of it under the skin of each side of the breast. Don't make your self nutty trying to spread it all the way down the breast, the butter will melt once in the oven and do that work for you, and that's the point.
Take the remaining 1/4 of the butter mixture and spread over skin of the legs, no need to try and get it under the skin there. Place the halved onion and halved lemon inside the cavity. Arrange the chicken on top of the potatoes, fennel and carrots in the roasting pan, douse the chicken with the white wine and place in the oven and roast for about an hour and 40 minutes, until the chicken is cooked through and the juices run clear.
Remove from the oven and cover loosely with a piece of aluminum foil and let the chicken rest for 10 minutes. Carve chicken. Arrange the chicken and vegetables on a platter. Soak sliced bread in drippings and surround the platter with soaked crusts of bread.