Some of the children’s birth records are listed in the Orleans Parish birth index. The parents’ names are listed as William Nicholas Batson and Grace Baker.
Birth certificates can be ordered from the Louisiana State Archives with the information below:
Grace Louise 7 Dec 1844 Volume 8 Page 161
Sarah Ann 5 Oct 1840 Volume 8 Page 160
Mary Jane 16 May 1843 Volume 8 Page 160
Birth certificates from that time period weren't quite the same as the ones we have now. They generally included the parents' names and the country of birth (sometimes the city of birth), and sometimes included the address of the parents.