In a large skillet, heat the olive oil over medium to medium-high. Place the chicken skin side down and set a timer for 15 minutes. Flip the chicken, set the timer for another 15 minutes, and add the onions, moving them between the chicken.
Once done, remove the chicken and set aside.
Pour in a splash of white wine and continue to caramelize the onion until golden brown.
Add the creme fraiche and mustard, stir well, and season to taste with salt and pepper if needed.
Put the chicken back in skin side up, along with its juices, and simmer an additional 5-7 minutes. Avoid touching the skin with the sauce to keep it crispy.