Is døra just an alternative to døren? I've not come across it before and assumed it was plural...
'dør' is a feminine noun. Feminine nouns end with -a in the definite singular case. However, all feminine nouns may be inflected as masculine nouns, which end with -en in the definite singular case.
Call me naive... but what does this have to do with romance?
Døren til hjertet hennes er åpen.