Typically, public schools are free to attend, but school districts do have policies with regard to who can attend which schools within their district (also known as school zoning). I recommend that you start your research with the school district. You can search in SchoolFinder to locate contact information for school districts and schools in New Orleans, LA. http://www.education.com/schoolfinder/
I'm also including some additional resources below to support your family. Congratulations on this special milestone in your child's education -- I hope he has a wonderful year in kindergarten!
I do not know about how Mississppi schools operate but first you should call the LA school dist. and see if they have a school of choice, If so then there should not have any fees all you would have to do is provide transportation.