Heat oven to 375°F Heat oil in a large ovenproof sauté pan over medium-high heat. Season chicken with salt, pepper and herbes de Provence. Dust with flour; tap off excess. Cook, meaty side down, 5 minutes. Turn over; cook 1 minute. Add garlic and shallot; stir 30 seconds. Add wine; cook 1 minute. Add stock; cook 30 seconds. Add lemon juice.
Transfer pan to oven. Bake until chicken is cooked through, 9 to 13 minutes. Transfer chicken to cutting board. Place pan over medium heat; simmer sauce 1 minute. Add butter; swirl pan until butter incorporates and sauce thickens slightly.
Cut each breast into 4 slices; transfer each to a plate; top with sauce and garlic. Serve with spinach; garnish with zest, if desired.