Specialties often appear on the most expensive menu, or only on the carte.
Often they involve a surcharge if the ingredients are luxurious. I don't have enough experience dining in Paris to swear this is the rule, but we did dine at Carre des Feuilliants some years back. At dinner we ordered the seasonal degustation and most expensive menu. It was superb and a great value, but expensive. A few years later we found ourselves eager to return, and decided to try the lunch special menu.