Bring a large pan of salted water to the boil and cook the linguine until just al dente.
Meanwhile, melt the butter in a large pan over a medium heat. Add the shallot and garlic, cooking gently until softened but not coloured. Stir in the crab meat, sun-blush tomatoes, crème fraîche, and Parmesan. Season well with salt and black pepper.
Using tongs, lift the pasta straight from the water into the pan, bringing some of the starchy pasta water with it. Toss everything together over the heat, adding an extra splash of pasta water if needed, until the sauce lightly coats the pasta.