Steam haricots verts, wax beans, and edamame, covered, 6 minutes or until haricots verts and wax beans are crisp-tender. Drain and plunge beans into ice water; drain. Combine beans, tomatoes, bell pepper, and onion in a large bowl.
Combine vinegar, sugar, and mustard, stirring with a whisk. Gradually add oil to vinegar mixture, stirring constantly with a whisk. Stir in parsley, salt, and black pepper. Drizzle vinaigrette over bean mixture; toss gently to coat.
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