Position a rack in the lower third of the oven and heat the oven to 400°F.
Trim any excess fat from the cavity of the chicken. Pat the chicken very dry and season inside and out with 2 tsp. salt and 1 tsp. pepper. Squeeze the juice from the lemon half and set the juice aside. Put the juiced lemon half in the chicken’s cavity. Cross the chicken legs and tie them together; tuck the wings under the chicken. Using a small sieve, dust the breasts and legs with the paprika.
Heat the oil in a 3- to 4-quart Dutch oven (large enough to fit the chicken snugly) over medium-high heat. Add the chicken, breast side down, and cook until the skin is browned, about 2 minutes. Turn and cook the back and sides until browned, 2 to 3 minutes per side. Transfer the chicken to a plate and pour off and discard the oil left in the pot.
Return the pot to medium-high heat. Add the garlic and wine to the pot, stirring to deglaze the browned bits from the bottom. Return the chicken to the pot, setting it breast side up on top of the garlic. Add the herbs to the pot, pour the broth over the chicken, and bring to a boil. Cover and transfer the pot to the oven. Cook, basting the chicken every 20 minutes, until an instant-read thermometer inserted in the thigh registers 160°F, 45 minutes to 1 hour.
Uncover and continue to cook the chicken until the thermometer registers 165° to 170°F in the thigh and the juices from the thigh run clear when the thermometer is removed, about 10 minutes more. Transfer the chicken to a cutting board and the garlic cloves to a serving platter; cover both loosely with foil to keep warm.
Strain the braising liquid from the pot into a small saucepan; discard the herbs. Tilt the pan so the juices collect in one corner and spoon off and discard as much of the fat as possible. Bring to a boil over medium-high heat. Simmer until reduced to 3/4 cup, about 5 minutes. Season to taste with salt, pepper, and some of the reserved lemon juice.
Carve the chicken and transfer the pieces to the serving platter with the garlic. Serve with the sauce and the baguette slices.