In a bowl, with a mixer on high speed, beat créme fraîche and coconut milk until soft peaks form. Cover and chill while preparing shallots and scallops.
In an 8- to 10-inch nonstick frying pan over medium heat, stir shallots in oil until crisp and golden, 6 to 10 minutes. With a slotted spoon, transfer to a paper towel to drain.
Rinse scallops and pat dry. Sprinkle both sides with salt and pepper. Add scallops in a single layer to frying pan (no need to wash) and cook, turning once, until browned on both sides and barely opaque but still moist-looking in the center (cut to test), 3 to 4 minutes total. Let cool to room temperature, about 5 minutes.
Arrange scallops on a platter and top each with about 2 teaspoons coconut crème fraîche. Sprinkle equally with fried shallots.