Heat oven to 400° F. Toss the beets, potatoes, fennel, 2 tablespoons of the oil, and ½ teaspoon salt on a rimmed baking sheet. Roast, tossing once, until tender, 24 to 28 minutes. Let cool.
Toss the roasted beets and potatoes, mâche, avocados, cornichons, lemon juice, the remaining 2 tablespoons of oil, and ½ teaspoon each salt and pepper in a large bowl.
Serve the salad with the Brie and bread.