Preheat the oven to 325°F. Bring a large pot of salted water to a boil. Trim the stalks from the fennel and set aside. Peel the bulbs and cut each one, root to tip, into 4 even slices. Boil the fennel slices for 4 minutes, or until just cooked; strain and pat dry (you can reserve the boiling water for the cherry tomatoes). In a bowl, toss the fennel with olive oil to coat and season with salt, pepper, piment d’Espelette, and 1 tablespoon of the herbes de Provence.
Score the skin of each fish fillet 3 to 4 times and season them on both sides and in the cavities with salt, pepper, piment d’Espelette, and 1 tablespoon herbes de Provence.
Stuff each fish with the reserved fennel stalks, half of the sliced lemon, and half of the sliced lime.
In the bottom of a baking or roasting dish large enough to hold the fish, combine the 4 cups kosher salt, the remaining ¼ cup herbes de Provence, the sliced lemons and limes, and ½ cup water. Top the salt mixture with a sheet of parchment paper and poke it several times with a knife. Line the fennel around the outer edges of the dish and nestle the fish into the middle with their bellies facing in. Cover with aluminum foil and bake for 20 to 30 minutes, until the thickest parts of the fish fillets reach 120°F. Remove from the oven and rest for 5 minutes before carving off the fillets.
For the Grape Sauce Vierge
Score the bottoms of the cherry tomatoes with an X and boil for 5 seconds. Rinse with cold water and peel the skins. Halve the tomatoes and put in a large bowl. Add the remaining ingredients.
Serve the fish fillets with the fennel and drizzle grape sauce vierge on top.