No private parking, there is public parking within 300 feet, but it does cost.

You can at your own risk

Cheaper to park at the French Market parking, then walk the pier/boardwalk to the aquarium. Get to see the water and riverboats while on the way there.

Parking in Canal Place Garage is close, a large surface pay lot is available, the casino has a garage. Parking can be validated by the Aquarium for a discount.

You can park farther away for free and take the streetcar

You can but I wouldn’t

Does the aquarium validate your parking? And if so where should I park?

Depends where you park them have paid and free parking around the area