Add the potatoes to a medium pot and cover with water. Add a few pinches of salt. Place on the stove and set to medium-high heat. Bring the potatoes to a low boil and cook until just tender when pierced with a fork, about 18 minutes. Remove from the pan with a slotted spoon and place in a colander or on a sheet pan lined with a towel to drain.
Meanwhile, prepare an ice bath and set aside. With the water at rolling boil, add the haricots verts and cook until tender but still crisp, about 2 minutes. Remove from the pot and immediately submerge in the ice bath to shock. Drain when ready to use, making sure they are very dry.
Using a sharp paring knife, score the fat in the duck breasts a couple times in two directions to create a crosshatch pattern. Cut through the fat but not into the meat of the breast. Salt the breasts and let sit outside the refrigerator for 10 to 15 minutes to allow them to come to room temperature.
Add the olive oil to a large saute pan. Place the duck in the pan skin-side down. Bring the pan to medium heat and cook the duck breasts low and slow to allow the fat to render and the skin to get nice and crispy. As the fat renders out of the duck, pour or spoon it out of the pan and set it aside. Cook the duck for 8 to 9 minutes on the skin side. Turn the duck over and cook the duck for 2 to 3 minutes on the flesh side. Remove the duck from the pan, cover with foil and let rest for about 10 minutes.
Add the shallots to the pan and cook until just translucent, about 3 minutes, adding a bit of the reserved duck fat if pan is too dry. Then, add the white wine, chicken stock and mustard. Bring to a boil, then reduce to a simmer and let cook until the sauce has reduced by half and coats the back of a spoon, about 3 minutes. Taste and season with salt and crushed red pepper.
Meanwhile, add the remaining duck fat to a separate large saute pan (if the ducks were lean and there isn't enough fat to generously coat the pan, add a bit of olive oil) over medium-high heat. Add the thyme sprigs and potatoes, cut-side down and cook until they begin to brown on all sides, about 7 minutes. When potatoes are brown and crisp, remove from pan and set aside. Discard the thyme. Add the garlic and cook for a minute, making sure it doesn't brown. Add the drained haricots verts and saute with salt and crushed red pepper. Remove from the heat.
Slice the duck breast thinly on the bias. Add a handful of frisee to plate or platter. Top with the potatoes and haricots verts, then the sliced duck breast and finally the pan sauce. Serve!