Rinse and drain the kidney beans and cannellini beans. Place the kidney beans, cannelini beand, and thawed green beans in a bowl.
Slice the red onion, then soak the onion in a bowl of ice water for about five minutes before draining and finely dicing. Chop the parsley. Add the onion and parsley to the bowl with the beans.
In a separate bowl, whisk together the vinegar, sugar, olive oil, salt, pepper, and Dijon.
Pour the dressing over the beans, onion, and parsley, then stir to combine.
Transfer the bean salad to the refrigerator and let the beans marinate in the dressing for about 30 minutes before serving. Give the salad a good stir just before serving to redistribute the dressing.