1Combine onion, celery, carrot, 1 tablespoon olive oil, chopped garlic, lemon zest, 3/4 teaspoon salt, pepper, saffron, fennel seeds, and herbes de Provence in a bowl; add chicken and turn to coat. Cover bowl and refrigerate until flavors combine, at least 15 minutes.
2Transfer chicken mixture to a stainless steel pot; add potatoes, tomatoes, water, and white wine. Cover and bring to a boil; reduce heat to low and simmer for 25 minutes. Add sausage and cook for 5 minutes. Stir tarragon and liqueur into pot.
3Remove half of a cooked potato and 1/4 cup liquid from the pot and place in a food processor; add peeled garlic, paprika, and cayenne pepper. Process until smooth, about 10 seconds. Add egg yolk and keep processor running; pour in 1/2 cup olive oil slowly until incorporated and rouille is smooth. Season with salt.
