For pre-1820 arrivals, you can try the Passenger and Immigration Lists Index edited by P. William Filby, which lists arrivals at many ports. It’s available on Ancestry.com. A book, New World Immigrants, edited by Michael Tepper, includes a list of passengers leaving France for Louisiana, 1718 to 1724, originally published in the Louisiana Historical Society Quarterly. New Orleans passenger lists from 1813 also have been transcribed at GeneSearch.com.
Q. How can I find very early New Orleans passenger lists?
A. The National Archives has compiled Passenger lists for arrivals through the port of New Orleans in two microfilm publications. The earliest records, 1820 to 1902, are in publication M259. Records for 1903 to 1945 are in publication T905. You can now search these lists on FamilySearch.org. Ancestry.com also has these collections as well as related records. Some of these records may actually predate the 1820 US government requirement that arriving foreign vessels provide passenger lists.
Another source that may help identify early arrivals to New Orleans is the CD collection Early Louisiana Settlers, 1600s-1800s (Genealogical Publishing Co.). Though not specifically a collection of passenger records, this CD includes data on early families, military records and French marriages, as well as lists of 500 passengers arriving in 1719 and 1720 and migrants from the Canary Islands, 1778 to 1783.
From the September 2013 Family Tree Magazine