Prepare an ice-water bath. Cook green beans in boiling salted water, just until bright green and tender, about 5 minutes. Reserving the cooking liquid, remove beans with a large slotted spoon; transfer to ice-water bath to stop the cooking. Transfer beans to a colander. Cook butter beans in the boiling cooking liquid, just until tender, 5 minutes if frozen. Strain; place under cold, running water to stop cooking. Set aside.
Make vinaigrette: In a medium bowl, combine vinegar, mustard, salt and pepper to taste, and minced shallot. Whisk in olive oil until vinaigrette is creamy. Whisk in tarragon and parsley.
In a large bowl, toss green beans until well coated with about three-quarters of the vinaigrette. In a large bowl or on a platter, arrange the green beans in an even layer. Sprinkle the reserved butter beans over the top. Drizzle the remaining vinaigrette over the beans. Garnish with tarragon and parsley. Serve at room temperature.