The first new state in the United States to be organized after the independence of the British colonies was the State of Franklin. This frontier district in the Appalachian and Cumberland Mountains declared itself independent of North Carolina in 1784. It lasted until a brief civil war in 1788, when it was reabsorbed into North Carolina. The region was later to become part of Tennessee.

At this time the United States extended nominally as far west as the Mississippi River, but the western regions were Indian territory. What is now Tennessee was then part of North Carolina. The US Constitution had not yet been ratified, so the states were independent countries in a loose confederation, and state justice did not run all the way west. North Carolina was especially reluctant to join the Union. The few settlers west of the mountains, around Fort Watauga, felt very unsafe.

North Carolina being impoverished and unable to support the settlers in their wars against the Cherokee and other tribes, in 1784 agreed to cede to the Federal Government all their western territory (present-day Tennessee). They quickly had second thoughts and passed a second law, retaining control temporarily and ceding it to the US only when the US Congress should agree to take it and their debts on, giving them two years to do so.

At this point the settlers in the valleys of the Clinch and Holston Rivers took matters into their own hands, and the counties of Sullivan, Washington, Greene, and Davidson agreed to secede from North Carolina. On 23 August 1784 delegates from the first three counties meeting at Jonesboro declared the independent State of Franklin.

(Counties of those names still exist in upper eastern Tennessee, but Davidson County is the one around Nashville much further east, so I'm guessing it's not the original Davidson.)

One proposal for the name was Frankland, "Land of the Free". This was altered to Franklin in a neat political pitch for the support of Benjamin Franklin, who replied politely but noncommittally to their letters (in 1787):

I am sensible of the honor which your Excellency and your council do me. but being in Europe when your State was formed I am too little acquainted with the circumstances to be able to offer you anything just now that may be of importance, since everything material that regards your welfare will doubtless have occurred to yourselves. ... I will endeavor to inform myself more perfectly of your affairs by inquiry and searching the records of Congress and if anything should occur to me that I think may be useful to you, you shall hear from me thereupon.
The provisional constitution, which specified that no-one could hold office "if he were immoral, a Sabbath breaker, a clergyman, a doctor or a lawyer", was drawn up by Sam Houston, father of the founder of Texas. In November 1785 a constitutional convention met at Greeneville, and a more moderate one was adopted, based very closely on that of North Carolina, at the instigation of Governor John Sevier. The legislature met, and organized taxes, county boundaries, courts, and Indian treaties.

Sevier's opponent was Colonel John Tipton, who had supported the vote of independence but did not want to organize as a new state. Discussion began of whether Franklin should join the Union at all, or move to full independence; contacts were made with Spain, the ruler of Florida. The state's early prosperity collapsed as Indian wars became more severe. Tipton started taking military action to restore the region to North Carolina. This culminated in several violent showdowns between the forces of Sevier and Tipton in 1788. Sevier fled, accused of treason, and Franklin was reabsorbed into North Carolina.

In 1789 the area became part of the Tennessee Territory, as North Carolina once more ceded it to the US government. Sevier and Tipton both became members of the North Carolina legislature, which ratified the Union in that year. When the State of Tennessee was admitted in 1796, both joined its assembly, and John Sevier was its first governor, serving 1796-1801 and 1803-1809.

More detailed information at: