Season chicken breasts with salt and freshly ground black pepper to taste.
Heat up olive oil in Dutch oven or pot over medium/high heat. Add garlic and shallots and sauté until nearly browned, 10-12 minutes. Add tarragon and sauté for 2 more minutes. Remove from the Dutch oven into a bowl, and set aside.
Lower heat to medium/low, heat up more olive oil and add chicken breasts. Cook for 5 minutes on each side, or until browned.
Add the tarragon shallots back into the Dutch oven, and pour in white wine. Cover and simmer for 10-12 minutes, turning chicken half way through.
Check the chicken is cooked through by making a small cut into the thickest part and ensuring the juices run clear. If not, simmer for a few minutes longer and check again.
Remove chicken from Dutch oven and allow to rest for a few minutes while you sauté the zoodles. Heat up olive oil in Dutch pan over medium heat and add in the garlic. Sauté until golden, 1 to 2 minutes. Add in the zoodles and cook until lightly softened (but not fully overcooked), 2 to 3 minutes. Mix in ricotta.
Serve ricotta zoodles right away, topped with the tarragon chicken and finished off with a touch more fresh tarragon, parmesan and freshly squeezed lemon juice (optional).
Please note that nutritional values are calculated for just the tarragon chicken with the ricotta sauce, as zucchini values vary by size and desired quantity (so your best bet for more accuracy is to weigh and factor them in yourself).