This is very interesting information. I've made copies of each of the documents you've provided, and intend to use them to help me sort out this family.. The first thing that I notice is that Uranie Hoffpauir has twice given births to and Baptized children without naming the father of the children. I find this both interesting and confusing. Second, the Nicholas birth only "fits" my exisiting people in my database to the Nicholas Hoffpauir that I have as the son of Ephraim Hoffpauir Jr. and his wife Julianne Joffrion. I therefore see 2 possibilities.... I have Nicholas entered to the wrong family, or this is a completely "new" to me Nicholas. The fact that Uranie has another child, Marie, could be the Mary Hoffpauir that I also have in the family of Ephraim and Julianne..... or again, it could be someone entirely new. French Catholic priests often used Marie instead of Mary, even if the family called the child Mary.
Also very important is the fact that the death certificate for Nicholas was signed by Emanuel Hoffpauir. Emanuel is known to be the son of Nicholas. I have Nicholas as married to Noalie Domingue and Mary Anna Dugas (with Noalie as the mother of Emanuel). His wife at time of death is listed as Ann Dugas, so this fits perfectly with my data.
So, there's more work to be done to try to find out who the father of Nicholas and Marie was. Is there any possibility of locating a death certificate or a baptismal record for Uranie?