Get a large Dutch oven on the stove over medium-high heat and add the duck fat.
Liberally salt and pepper each piece of chicken.
Add the chicken to the pot without crowding, you will likely need to brown in batches. Leave the chicken to truly brown (don't move it too much). This can take up to 8 minutes a side. Turn the chicken once they are easily moveable and don't stick to the bottom, repeating through all the chicken pieces.
Remove the chicken once browned and set aside.
Turn the stove to medium heat and add the carrots, leeks and shallot. If there is not enough fat in the pot, add a pat of butter. Cook, stirring frequently until tender, about 10 minutes.
Add the garlic and cook for just a minute more.
Add the fresh chopped tarragon and thyme, then add the wine and deglaze the pan scraping up all the little good bits until the wine is reduced.
Next add the chicken back to the pot with 4 cups of water. Turn heat up to get a boil, then down to a simmer. Simmer for one hour.
Add the drained beans to the pot and continue to simmer for another two hours until you can remove the bones from the chicken easily. Taste the beans for doneness.
Skim any fat off the top of the stew.
Add salt and pepper to taste.
Serve topped with a few more dashes of the fresh herbs and with crusty bread along side of the stew.