In a large pot, heat the olive oil over medium heat. Add the chopped shallots, carrots, and celery. Sauté for about 5 minutes or until the vegetables begin to soften.
Add the chopped mushrooms and sauté until they start to soften. About 3 - 5 minutes. Then add minced garlic and continue to sauté for another minute or until fragrant.
Stir in the herbes de Provence, capers, thyme, and diced tomatoes. Cook for a couple of minutes, allowing the flavors to meld.
Pour in the vegetable broth, and French green lentils, and add the bay leaf. Give it a good stir.
Bring the mixture to a boil, then reduce the heat to low, cover the pot with a lid, and let it simmer for about 35 - 40 minutes or until the lentils are tender but still holding their shape.
Once the lentils are cooked, remove the bay leaf. Stir in the lemon juice to brighten flavor and coconut aminos or tamari, if using, to add richness.
Taste the stew, add salt and pepper, and adjust the seasoning if needed.
Serve the French Lentil Stew hot, garnished with fresh parsley or fresh herbs if desired.