The Malus-Beauregard House was built in the 1830's. It sits just in front of the Rodriguez Canal and about 50 yards from the present-day Mississippi River levee.
I think the one you are referring to is Ignace de Lino Chalmette's plantation, but that burned down during the battle. I am not exactly sure where the house was located.
To make it more confusing:
The Chalmette Plantations (I believe there were five: Jumonville, Villere, De La Ronde/Versailles, Lacoste, and McCarty) that were on or around the area during the battle no longer exist.
The ruins of the De La Ronde/Versailles Plantation are the neutral ground- median in non-New Orleans terms between the opposing stretches of Judge Perez Highway. The land that the Battlefield Trust is trying to preserve is between the Chalmette National Cemetery and the chemical plants along the river..which is where I think Ignace de Lino Chalmette's plantation was located. The McCarty tract was where Jackson's lines were. The Jumonville area was where the British field hospital was, and the De La Ronde/Versailles Plantation served as Packenham's headquarters. The Villere plantation is about three miles down the road from the national park.