We think not. It's very easy to use Uber/Lyft to get around town. Parking downtown and in the French Quarter and other high-traffic areas can be tricky and expensive, so take this into consideration when deciding whether or not to rent a car.
We will provide transportation after the reception back to the hotels. Please plan to Uber/Lyft/taxi to the wedding venue. If you drive, there is ample parking in the lot closest to the Botanical Garden.