In a plastic bag, shake flour with 1/2 tsp. salt, 1/4 tsp. pepper, and the herbes de Provence; set aside.
In a 5- to 6-qt. pot over medium-high heat, brown bacon, stirring often, 6 to 7 minutes. Meanwhile, cut chicken into 1-in. chunks, then shake half at a time in flour to coat.
With a slotted spoon, transfer bacon from pan to paper towels. Brown half the chicken in bacon fat, stirring often, 3 to 5 minutes. Transfer to a plate. Repeat with remaining chicken, adding oil to pot. Meanwhile, halve carrots lengthwise and cut celery into diagonal slices. Chop onion.
Add vegetables to pot with remaining 1/4 tsp. each salt and pepper and sauté until onion is golden, about 5 minutes. Meanwhile, in a microwave-safe bowl, microwave wine and broth until steaming, about 3 minutes.
Add broth mixture, chicken, and bacon to pan, stirring to loosen browned bits. Cover and bring to a boil over high heat. Reduce heat and simmer until vegetables are tender, about 15 minutes. Meanwhile, coarsely chop parsley and tarragon. Stir them into stew.