Tennessee divided in half, with a Chattanooga based government controlling Franklin.
And why wouldn't Knoxville be the capital of this division, like Knoxville was of the entire state until 1817?
Plus if you want a Republican state, you just need to divide Tennessee somewhere along the Cumberland Plateau (like how TN nowadays defines "East Tennessee"). Including more of Tennessee would make this new state of Franklin a swing state or even a reliably Democratic state. I think the Republicans would like the two senators East Tennessee is almost always guaranteed to elect to counterbalance the two Democrat senators which Tennessee OTL almost always provided (even in the best years, Republicans found it very hard to mount a campaign during the time of the Solid South).
Or alternatively divide Tennessee along the West/Middle/East Tennessee distinction. Call West Tennessee "Jackson", East Tennessee "Franklin", leave Middle Tennessee just "Tennessee". But unless you protect the civil rights of the now freed Blacks in the state, that will guarantee you two Democrat states and four Democrat senators, amongst other political gains.
And that's a big problem, since unless you protect the rights of Black voters, you'll be giving more influence and power to Southern Democrats once they "Redeem" their states.