Cut bell pepper in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil for 10 minutes or until blackened. Place in a paper bag; fold to close tightly. Let stand 10 minutes. Peel and chop. Cook edamame and haricots verts in boiling water 4 minutes; rinse with cold water, and drain.
Combine bell pepper, edamame mixture, chickpeas, salt, and pepper in a medium bowl. Combine shallots and remaining ingredients, stirring well with a whisk. Drizzle dressing over bean mixture; toss.