Heat half the oil in a frying pan over a medium heat. Season the chicken with black pepper and add to the pan along with the onions. Cook for 10 minutes, turning occasionally, until golden. Remove from the pan and set aside.
Heat the remaining oil in the pan then add the mushrooms. Cook for 5 minutes, adding the garlic for the final minute. Return the chicken and onions to the pan with the stock and most of the tarragon.
Simmer for 10 minutes until the chicken is cooked through with no pink remaining. Boil or steam the mange tout 2-3 minutes before the end of cooking time.
Take the chicken off the heat and stir in the crème fraîche. Garnish with the remaining tarragon and serve with the mange tout and baguette pieces.