Historical buildings
People can do whatever they are willing to spend the time and money to do. When the Aswan Dam was built in Egypt, entire massive temple complexes were cut apart, numbered, and rebuilt on higher ground.
This would not be easy to do with a city, and even if you did, I suspect the result would a lot of its historical value. New Orleans is OLD, and that's more than just old buildings standing around. You'd probably end up with the kind of New Orleans you see in Disneyland.
The floodgate idea might work, or large barriers outside the city driven down to the rock underneath. I don't know enough about the geology or layout. But others do.
We need to see what ideas come out of this.