Float it.
Some years back I did some research and a bit of design on large-scale floating cities at sea, back when spaceports looked like they would have to go elsewhere to be allowed to operate.
There are functional designs for systems over a mile across for deep-sea use.
Rebuild the substructure of New Orleans on floating systems. Of course, when you price out moving New Orleans onto an artificial concrete mega-pontoon, you might find it would be cheaper to move the Mississippi into Arizona.
Face it, in reality, like ancient cities that kept rebuilding on the rubble of predecessors, the structure of New Orleans will rebuild bit by bit as the land and water move around. An eternal kludge. A city that is a process, not a final accomplishment.