Heat 1 tablespoon of oil in a small skillet over high heat. When the oil is hot but not smoking, add the shallots and sauté until soft, but not browned, 2 to 3 minutes.
Add the tomatoes and continue cooking until much of the liquid is gone, about 10 minutes. Reduce the heat to low and add the crème Fraiche. Season with salt and pepper. Warm the crème through and set aside.
Preheat the oven to 325ᵒ
Brush the salmon with the remaining olive oil all over. Preheat a 12 inch dry skillet over medium heat. Add the salmon and cook the salmon for 2 minutes. Season with salt. Turn the salmon over and cook for 2 more minutes. Season again with salt.
Place the skillet in the oven and bake until the salmon is opaque through, about 5 minutes more.
To serve, mince the basil and stir into the sauce. Spoon several tablespoons of sauce in the center of a warmed dinner plate and place the salmon on top of the sauce. Serve warm immediately.