Preheat oven to 425 degrees. Wrap beets in parchment, then foil, and place on a rimmed baking sheet. Roast until tender, about 60 minutes. Let cool completely. Peel and cut beets into 1/2-inch dice. Transfer to a large bowl.
Prepare an ice-water bath. Cook haricots verts in boiling salted water until bright green and crisp tender, about 2 minutes. Transfer to ice-water bath, and drain. Cut beans diagonally into thirds, and add to beets.
Mix vinegar, shallot, and mustard in a small bowl. Add oil in a slow, steady stream, whisking until emulsified. Toss with vegetables, and season with salt and pepper. Stir in torn basil and goat cheese. Garnish with basil leaves.