Bring the beets and enough water to cover to a boil in a large saucepan. Cook until fork-tender, 10 to 20 minutes, depending on size. Drain and cool.
Whisk together the oil, vinegar, salt, and pepper.
Use a paper towel to rub the skins off the beets; cut into wedges. Spread the crème fraîche on a serving platter or each of 4 plates. Top with beets, shallot, and pistachios. Drizzle with the dressing and serve at room temperature.