Heat oven to 350°F. Heat large Dutch oven on medium. Add pancetta and oil and cook until pancetta is browned, 3 minutes. Using slotted spoon, transfer to paper towel.
Pat chicken pieces very dry and season with 1/2 teaspoon each salt and pepper. Add skin side down to pot and cook until golden brown, 5 minutes per side. Transfer to plate.
Increase heat to medium-high, then add mushrooms and cook, tossing only twice, until browned, 6 to 8 minutes. Reduce heat to medium-low and add onions, leeks, and garlic and cook, stirring occasionally, until light golden brown and tender, 6 to 7 minutes.
Sprinkle with flour and cook, stirring, 1 minute. Add wine and bring to a simmer. Stir in broth, mustard, thyme, and bay leaves.
Return chicken and pancetta to pan, cover, transfer to oven and cook until chicken is fork-tender, about 11/2 hours. Remove from oven, discard thyme and bay leaves, and sprinkle with fresh tarragon.