In a small bowl, combine the salt, pepper, and 1 tablespoon Herbes de Provence.
Break apart the onion segments and spread them evenly on the bottom of the slow cooker. Top with the carrots, garlic, and green beans, if using.
Pat the chicken dry using paper towels. Press the spice mixture evenly on all sides of the chicken, as well as sprinkling some inside the cavity. Place the lemon quarters inside the chicken.
Place the chicken into the slow cooker. (Note: you might need to adjust the vegetables, moving some around the sides so the lid will close properly. For reference, I used a 6-quart slow cooker).
Sprinkle the additional teaspoon of Herbes de Provence on top and close the lid. Cook on high for 4-5 hours or low for 8-9 hours.
When the chicken has finish cooking, it will still be in tact, but will fall apart very easily. With a large bowl directly next to the slow cooker, use tongs to transfer the chicken. It’s ok if it breaks apart; this might need to be done in stages. Separate the meat from the bones. Shred the chicken delicately using two forks.
Serve chicken with the vegetables (discard the lemon wedges), and drizzle the liquid on top.
Notes
If you like serving meat and potatoes together, try adding 2 cups quartered red potatoes (skin on) to the slow cooker.