The heart wants what it wants, and if you are both certain this is what you want to do, the chaplain is exactly the right first point of contact.
Call Bledsoe County Correctional Complex and ask to speak with the facility chaplain. Explain that you and your fiancé want to get married and ask what the process is for requesting a marriage ceremony. The chaplain handles these requests regularly and can tell you what paperwork needs to be submitted, what approval is required from administration, and what the timeline typically looks like. In most Tennessee facilities the request goes to the warden for final approval, and having a clean disciplinary record inside works strongly in your fiancé's favor when that review happens.
On the civil side, you will need a marriage license from the county clerk in Bledsoe County before the ceremony can take place. The requirements are the same as any other Tennessee marriage license. That paperwork needs to be in order before any ceremony is scheduled.
That said, the original advice here is worth genuinely considering before you make the call. A prison ceremony happens in a visitation room, usually brief and with very limited guests, and the photos will reflect the setting. That is a memory that lives with you permanently. Many couples in exactly your situation choose to have a small private ceremony after release that gives them real wedding photos, a real venue, and the ability to celebrate with the people who matter to them without the constraints of a correctional facility.
Neither choice is wrong. The question worth sitting with is which version of that memory you want to carry for the rest of your life together.
If you decide to proceed, start with the chaplain. That is the right door to knock on first.