Pat the chicken dry with paper towels and sprinkle with salt and fresh pepper on both sides.
Heat 1 tablespoon olive oil in a large (11-12 inch) skillet over medium heat. When hot, place the chicken skin-side down and cook without moving for 15 minutes, until the skin is golden brown. Flip and cook another 15 minutes (until internal temp is 155-160F), then remove and set aside.
Add the onions to the pan and cook until caramelized, about 30 minutes. Add the wine and cook until almost all evaporated. Stir in the creme fraiche, Dijon mustard, and whole-grain mustard until combined. Salt to taste.
Return the chicken thighs to the pan along with their juices. Sprinkle with parsley and serve hot.