Preheat the slow cooker if necessary; see the manufacturer's instructions. Wash the chicken inside and out with cold water and pat dry with kitchen paper. Heat the oil in a large frying pan, add the chicken, breast side down, and fry for 10 minutes, turning the chicken several times until browned all over.
Put the chicken, breast side down, in the slow cooker pot. Fry the onion wedges in the remaining oil in the pan until lightly browned. Add the cider, mustard and sugar and season with salt and pepper. Bring to the boil, then pour over the chicken. Add the hot stock, then the vegetables, lemon wedges and 3 sprigs of the tarragon, making sure that the chicken and all the vegetables are well below the level of the stock so that they cook evenly and thoroughly.
Cover with the lid and cook on high for 5–6 hours or until the chicken is thoroughly cooked and the meat juices run clear when the thickest parts of the leg and breast are pierced with a sharp knife. Turn the chicken after 4 hours, if liked.
Lift the chicken out of the stock, drain well and transfer to a large serving plate. Remove the vegetables with a slotted spoon and arrange them around the chicken. Measure 600 ml (1 pint) of the hot cooking stock from the slow cooker pot into a jug. Reserve a few sprigs of tarragon to garnish, chop the remainder and whisk into the jug with the crème fraîche to make a gravy. Adjust the seasoning to taste. Carve the chicken in the usual way and serve with the gravy and vegetables. Garnish with lemon wedges, if liked, and the reserved tarragon sprigs, torn into pieces.