I dont think this is all that hard. If you have studied spanish you can loosely compare "Avisen" and "En Avis" to the rules regaurding "El" and "la"/ "un" and "una" in Spanish pronouns are genderized. El is the singular masculine term for generalizing single masculine objects both animated and non animated. An example would be El nino or the boy or El libro which means the book. For feminen objects animated or non animated they use "La". Examples for this would be La nina for the girl and La casa for the house. Remember that both "El" and "La" are genderized generalizations. If you want to be more specific you can use "Un" or "Una" both of which come from "Uno" which is that spanish word for one. Gender rules still apply, so from the examples above El nino (the boy) becomes Un nino (a boy or one boy) and La nina (the girl) becomes Una nina (a girl or one girl).
So if you think about it you can loosely equate Avisen (the newspaper) to El periodico (the newspaper in spanish) and En avis (a newspaper) to Un periodico (A newspaper). There are a couple problems with this so use it at your own risk. Fristly i notice that Avisen can be both "the newspaper" and "newspapers" and that examples like tjis are random and not gender specific in Danish, atg least that ive picked up on. Second Spanish has a different terms for plurals or groups of objects (los ninos = the boys and las ninas = the girls) that are seperate from the singulars, literally the word for the subject will change along with the article. Sorry if I confused anyone more then helped them, it all made sense in my head.