Put the flour in a shallow dish and season with the thyme, salt and pepper. Dredge the chicken in the flour, shaking off the excess. Heat the EVOO in a Dutch oven over medium-high heat. Add the chicken and cook until browned and crisp on both sides. Remove to a plate.
Melt the butter in the pot over medium heat. Add the mushrooms and cook until lightly browned. Add the shallots, carrots and sugar, and season with salt and pepper. Cook for a couple of minutes to soften. Deglaze with the wine, stirring and scraping up any browned bits from the bottom of the pot with a wooden spoon. Stir in the tarragon, olives and tomatoes and bring to a simmer. Return the chicken to the pot and cook, partially covered, for 30 minutes, stirring occasionally.
Preheat the oven to 350 degrees F.
Slice the baguette on an angle and toast in the oven. Divide the chicken and sauce among plates and serve with the baguette.
Cook's Note: The stewed chicken can be covered and refrigerated for a make-ahead meal. Reheat over medium heat.