The 1900 census record is here:https://www.familysearch.org/search/image/show#uri=https%3A%...
It shows Eugene E(mile) Smith married to Emma (Alphonsine Green) since 1892 (the marriage record is also available through Family Search and shows them marrying 25 June 1892 in St. Tammanay, LA).
The only child living with them is Enola T. Smith, born June 1893. In other words, Enola is likely the daughter of Emma, not Hattie.
I also found a reference to Eugene Emile having married Hattie in 1888, but she must have been his first wife and either died or divorced.
Eugene Emile Smith, Jr. was born in 1902 and is likewise likely the son of Emma, not Hattie.
I have found no other references to a child named Frank Emile. Possibly he died young, or if Hattie and Eugene were divorced, went to live with her.
I hope this helps you!