Soak the flageolet beans in plenty of water for about 12 to 16 hours at room temperature. (They will look thoroughly plumped when they are ready to cook.)
Drain and rinse the beans. Place them in a large pot along with the garlic, thyme, and bay leaf. Add enough water to cover the beans by about 2 inches.
Bring to a boil and then reduce the heat to a gentle simmer. Cover the pot with a lid and cook for about 1 hour, or until the beans are tender.
In the meantime, prepare the rest of the salad ingredients. Quarter the tomatoes, roughly chop the olives and parsley, and finely chop the shallot for the dressing.
For the dressing, place the olive oil, vinegar, mustard, shallot, salt, and pepper in a small bowl. Whisk until combined.
When the beans are tender, drain and place them in a large bowl. Discard the garlic, bay leaf, and woody remains of the thyme sprigs. (But don't worry about all those little thyme leaves now flecked throughout the beans.)
Add the dressing to the hot beans and toss gently to coat. Then add the tomatoes, olives, and parsley, tossing everything briefly to combine. Taste for seasoning and serve.