Sprinkle the chicken with salt and pepper. Dredge the chicken in the flour to coat lightly. Shake off any excess flour. Melt 2 tablespoons of butter in a heavy large skillet over medium heat. Add the chicken and cook until brown, about 5 minutes per side. Transfer the chicken to a plate and tent with foil to keep it warm.
Melt 2 tablespoons of butter in the same skillet over medium heat. Add the shallots and garlic and saute until the shallots are translucent, stirring to scrape up any browned bits on the bottom of the skillet, about 1 minute. Add the wine. Increase the heat to medium-high and boil until the liquid is reduced by half, about 3 minutes. Add the cream and boil until the sauce reduces by half, stirring often, about 3 minutes. Stir in the parsley. Season the sauce, to taste, with salt and pepper. Add the chicken and any accumulated juices to the sauce, and turn the chicken to coat in the sauce.
Meanwhile, melt the remaining 2 tablespoons of butter in another large skillet over medium heat. Add the spinach and saute until heated through. Season the spinach, to taste, with salt and pepper. Arrange the spinach over a platter. Place the chicken atop the spinach. Pour the sauce over and serve.