Bring a large pot of water to a boil with the thyme sprig, coarse gray salt, and peppercorns. Add the langoustines, bring back to a boil, and cook for 2 minutes. Remove with a slotted spoon and set aside to cool.
Trim the green beans and cook in boiling salted water, uncovered, for about 15 minutes. Drain and immediately plunge into a bowl of ice water to preserve their vibrant color and crunch. Drain thoroughly.
Peel the carrots and cut into thin julienne strips. Blanch in boiling salted water for 1 minute, then refresh under cold water and drain well.
Wash the salad leaves and radishes thoroughly. Drain the leaves and slice the radishes into thin rings.
Carefully shell the langoustine tails, keeping them intact for an elegant presentation.
Peel and finely chop the shallot. Prepare the dressing by whisking together the balsamic vinegar, violet Brive mustard, shallot, olive oil, salt, and freshly ground pepper until emulsified.
On a large serving platter, artfully arrange the salad leaves, green beans, carrot julienne, radish slices, and langoustine tails. Drizzle with the dressing at the last moment, gently toss to combine, and serve immediately.
