The usage of English words always depends on context, context, context.
Consider that "North" is a compass point, "north" is a direction and "northern" is an adjective. We often use north and northern interchangeably.
Here are a FEW of the ways I can think to use these:
1. I live IN the north. => in the large area of the world to the north of here, probably far away. This is very vague.
I live IN the northern part of France. (inside France, northern half)
I live IN the northern hemisphere. (top half of the Earth)
2. A city has four sides (quadrants relative to the center point really -- NESW).
I live ON the north(ern) side of the city. He lives ON the south(ern) side.
France borders Spain ON the north (side).
3. France borders Spain TO the north. (that is, "on the north side")
4. France and Spain share a border. France's southern border is Spain's northern border.
France borders Spain ON the north.
France is located TO the north of Spain.
France is north of Spain.