The same ones that have always been native to New Orleans .... That is, the definition of native is plants that were there when Columbus discovered America. So what was native in 1930 is the same thing that was native in 1492 and also now. Some plants become "naturalized" but they still are not "native".

I think the Louisiana Native Plant Society web site might give you some good references (the following page has a good book). It also has a downloadable PDF file with the following caveat:

Note: this file does not indicate which species are native and which are naturalized, please go to http://plants.usda.gov for this info.

Here is a link that might be useful: Louisiana Native Plant Society

There are many many trees and shrubs native to the gulf coast that might have grown wild in New Orleans in the 1930s or now. In addition, the lcimate in New Orleans allows a very wide range of non-native plants to grow there, so there are many dozens of non-native trees and shrubs that grow in the city, especially in gardens or former gardens. Today a fair number of the common 'wild' shrubs around New Orleans are non-native, invasive species that were probably also there in the 1930s.