Heat the olive oil and 1 tablespoon of the butter in a large sauté pan over medium heat.
Season the chicken on both sides with salt, pepper, and Herbes de Provence. Lightly dust each piece with flour, shaking off any excess.
Sear the chicken in the pan for 2 to 3 minutes per side until golden brown and cooked through. Remove to a plate and set aside.
Add the mushrooms and chopped shallot to the same pan. Sauté for 12 to 14 minutes until the mushrooms are deeply golden and the shallot is softened.
Deglaze the pan with the red wine, scraping up any browned bits. Add the chicken stock and simmer for about 5 minutes until slightly reduced.
In a small bowl, mix together the remaining 1 tablespoon butter and 1 tablespoon flour to form a paste. Whisk it into the sauce and simmer for 1 to 2 minutes until thickened.
Return the chicken to the pan and spoon the sauce over the top. Simmer for 2 to 3 minutes to warm through.
Transfer to a serving platter, scatter with fresh herbs, and serve immediately.