Season the chicken well with salt and pepper. In a large skillet, heat the oil over medium-high heat; add the chicken, and fry until brown. Turn chicken and add the onion and garlic, saute until softened, about 5 minutes. Add the carrot; sprinkle with salt and pepper, Herbes de Provence, and tarragon.
Add the wine and simmer until reduced by half; about 5 minutes.
Add chicken stock, reduce heat; cover and simmer 15 minutes. Uncover and add the peas; continue to cook 5 minutes longer, or until the chicken is cooked through.
Meanwhile, bring a large pot of water to a rolling boil.
Remove the cooked chicken to a platter; keep warm.
Add the gnocchi to the boiling water, when they rise to the surface, remove with a slotted spoon; add to the sauce in the skillet; simmer for 2 to 3 minutes, mixing gently with the sauce until well coated. Taste, adjust seasonings and serve along-side the chicken.