The Spanish and French left their mark on the legal traditions in Louisiana (The Napoleonic Code). Civil Law Notaries and Catholicism provide records from the early colonial period. Thanks to Dr. Gwen Midlo-Hall for giving us a glimpse of the volumes of documented

Civil Law Notaries were used to record contracts, property transfers, wills, estates and births/acknowledgements. Their records are stored at the Notary Archives. If you found info on Dr. Hall's database, go to the source. The details may provide additional clues.

Catholic records include baptisms (and recordings of births), confirmations, marriages and deaths. Look at the Mobile Records, Kankakee (IL) and some Spanish records for early Orleanians of color - as well as the Santo Domingo
The New Orleans Archdiocese is the repository of some of these records, although several books and extracts have been published. Check Hebert publications as well as the Louisiana Genealogical Society for a list of available pubs.

For example, I found the index to the 'Confirmaciones' of St. Louis parish (Hebert) listing a Francisco (Francois) and Juan (Jean)TOMASIN. The parents MAY be Carlota and Juan TOMASIN (indexed as parents with same page ref).

In addition, the City of New Orleans kept Civil birth and death records. Did you find Carlotta/Charlotte in the Death Records Index online? The New Orleans site lists a Charlotte Dede Thomassin, who died in 1835 at 60 years old. The death record can be ordered from the LA State Archives in Baton Rouge.
I couldn't find a listing for a civil birth record for Francisco or Juan, but there were quite a few Thomas/Thomassin fpoc (Admiral, Eugenie, Thomas, Louis...). There was a listing of a Francois Thomassin, b. Mar 1821 - too late to be the son of the Carlotta on Colonial times (?). She would have been close to 50 years old then (46). The parents of Francois were Thomas and Marie Joseph, free people of color. [Could Charlotte have been Marie Charlotte?]

The New Orleans public library is the repository of many city documents. Contact their Louisiana/Genealogy division - one of the archivist specializes in LA Colonial free People of Color. Although they don't do research, they DO know the available resources and can help you determine your next step.

Others on this board are researching the free people of color in Louisiana colonial times. They will surely have first hand experience to share using colonial records from South Lousiana and New Orleans.

Good luck!