Bring a medium pot of well-salted water to a boil. Working in batches, blanch haricot verts and yellow wax beans until crisp-tender, about 3 minutes for each. Transfer to an ice bath. Drain. Cut beans into 1/2-inch pieces; transfer to a bowl.
Add white beans, red pepper, and arugula.
In a small bowl, whisk vinegar and oil. Season with salt and pepper. Drizzle over vegetables and toss to combine. Sprinkle with Parmesan before serving.