Circular Reasoning is indeed a type of logical fallacy, but your example opens the door because it uses a False Strawman.

The argument for Christian Scriptures being infallible is not made in a way that is circular, as you claim:

1. Archeological evidence proves that we know exactly what the original Bible authors wrote.
2. I judge what they wrote to be at least as credible as any other historical account.
3. I consider the possibility that they may all be fiction and find that to be less credible.
4. I decide to believe them at least as much as any other widely accepted historical account.
5. This means there probably really was Someone named Jesus who did amazing things.
6. I conclude His teachings have more credibility than any other person I know.
7. I encounter a teaching that I don't agree with. I search for an expert that can convincingly tell me I can ignore the teaching of Jesus. There is no such expert, including my own laughably amateur self, that I can find with greater credibility than the original authors I have decided to believe.
8. I realize that for all practical purposes the Scriptures are infallible because no one exists with the credibility to challenge them.

This is not circular reasoning. It is weighing evidence and finding evidence against Scriptures to be less compelling than evidence for it.

Maybe we should come up with an official name for this form of logical fallacy.
Hmmm. How about "Faux-circular Reasoning Ad-Hominem Strawman"?

It really needs a name, because I hear it all the time and just shake my head.