It is north of the capital county of Wake and was formed from a now defunct county, Bute. It is to the right of Granville County. Granville, Franklin and Wake share a border, which makes it a lot of fun/grief when researching ancestors who thought nothing of hopping across county lines as they farmed, raised families, and made corn liquor.
For example, my mother was born in Franklin County. Her middle sister was born in Granville, and her youngest sister was born in Wake. And the family probably moved just a mile or so down the road between children.
Note! Do not confuse Franklin County with Franklin, NC. They are at separate ends of the state.