In a plastic bag, shake flour with 1/2 teaspoons salt, 1/4 teaspoons pepper, and the herbes de Provence; set aside.
In a 5- to 6-qt. pan over medium-high heat, brown bacon, stirring occasionally, 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 occasionally, 3 to 5 minutes. Transfer to a plate. Repeat with remaining chicken, adding oil to pan. Meanwhile, cut carrots in half lengthwise and cut celery into diagonal slices. Chop onion.
Add vegetables to pan with remaining 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.