Hurricane Betsy caused a levee to break in New Orleans in the 1960s, and people who lived through that have stories to tell.
In one case, a family had to get on the roof of the house because any lower point was in water.
The people had to fight critters and creatures for the roof -- snakes and other things wanted the high ground. It was very unpleasant from what I remember of these stories.
With the infrastructure improvements in New Orleans proper in the past 25-30 years, I wouldn't worry too much about the city itself--unless a "hand of God"type storm hit the city--and a lot more about the suburbs on the West bank (they are not as far below sea level as some areas of New Orleans, but have less protection from the waters breaking over the levee) as well as over in Kenner and Westwego, because they fall right along the Bonnet Carre Spillway which diverts flood waters and storm surge from the Mississippi river just northwest of New Orleans into Lake Ponchartrain (and because it's a salt water lake, killing much of the aquatic life in its path)..
My dad grew up in N.O. and told me about Betsy.
Hurricane betsy became a tropical depression over land, came out on the atlantic on the eastern seaboard and returned to cat 2 hurricane status and gave NYC trouble before fizzling out in the cold north atlantic.