In a large bowl, mix together the ½ cup of Dijon mustard with the paprika, pepper, salt, and chile pepper flakes (if using). Add the chicken pieces and toss them in the mustard-spice paste, lifting the chicken skin and getting some of the paste underneath.
Place your largest, widest skillet or Dutch oven over medium-high heat. Add the diced bacon, and cook, stirring frequently, until it is cooked through and starting to brown. Remove the bacon with a slotted spoon and place on a paper towel-lined plate. Reserve 1 tablespoon of bacon fat and set aside the rest (or keep for a different use).
Add the diced onion and cook until it becomes soft and translucent, about 5 minutes. Stir in the thyme, continue cooking another few minutes, then scrape the onion-thyme mixture into a large bowl.
Add a little of the reserved bacon fat (or olive oil), and place the chicken pieces in the pan in a single layer. If they don't all fit, fry them in two batches. Continuing to cook over medium-high heat, brown the chicken pieces well on each side. The coloring that you are adding to the chicken (and the dark layer (fond) forming on bottom of the pot) is the source of the flavor of this dish.
Remove the chicken pieces from the pan, and add them to the bowl together with the onions. Slowly add the wine to the hot pan, using the liquid and a flat wooden utensil to scrape up the darkened layer on the bottom of the pan. This may take a few minutes and seem hopeless, but keep trying (gently) and you'll be pleasantly surprised. Once you have the dark bits incorporated into the liquid, return the chicken pieces to the pan, as well as the onion and bacon pieces. Reduce the heat to medium-low, cover the pan, and stirring occasionally, cook for about 15-30 minutes (depending on your particular chicken pieces), until the chicken is cooked through.
Take the pan off the heat and add the final 3 tablespoons of Dijon mustard, the whole grain mustard/mustard seeds, and the creme fraiche/cream. If you find the sauce to be too thick, add a little warm water (or chicken stock) to loosen it. Sprinkle the chopped parsley or chives over the top and serve, ideally over fresh pasta or another starch (see headnote for more suggestions).