Blanche definitely represents the Old South. She even grew up in a stereotypical Southern mansion and was encouraged to behave like a stereotypical Southern belle. She is not emotionally equipped to cope with the modern world. She needs to be sheltered and protected, as women used to be in the Old South. Her mind is filled with romantic notions. She expects men to treat her with old Southern chivalry and gallantry.
Stanley, on the other hand, does not necessarily represent the North. More likely he is intended to represent the "New South" which is becoming more and more like the North because of the transition from agriculture to industrialization. We understand why Blanche is living in the South, but it is never quite clear why Stanley is living in New Orleans rather than in some city like Chicago or Pittsburgh. He doesn't have any roots in the South; he just happened to end up there. More than representing the North, Stanley represents the social evolution taking place in the South, which includes the decline of the old aristocracy and the ascension of the proletariat.
William Faulkner often wrote about the contrast between the Old South and the New South, notably in the so-called "Snopes Trilogy," consisting of The Hamlet, The Town, and The Mansion. The decline of the Old South and the rise of the drastically different New South is a favorite theme with Southern writers.
Blanche is fading just as the South faded from its once glorious days of southern belles and dances on the veranda. Blanche has her memories back in the South and longed for the days that had passed. Blanche came form a southern mansion and she lost it due to her financial difficulties. She wants to be back in the lifestyle and adorns herself as if she still lived in the mansion. She uses the language of southerners in her flirtatious presentations.
Stanley accentuates the industrial Nouth. He is a Polish descendant from the mixed group of northerners. He is a hard worker and a laborer. He is used to the urbanized way of life that was common in the North after the industrial Revolution. In these ways he represents the North.