Florence to Terantola by train, to pick up car

The name of the town is spelled "Terontola"

There are no rental car offices in Terontola. The closest locations are Chiusi or Arezzo. However both do not have large busy offices with enough American tourists renters to justify keeping automatic rentals, therefore automatic cars may not be available at those locations..

All Europeans must take the driving test on manual cars (otherwise they put a stamp on your license that you can drive only automatic cars). There is sort of a stigma I guess, since that stamp was associated with disabled drivers who, because of some disability, could not drive manual transmission. For that reason, and because of the higher cost of purchase and maintenance, Europeans don't like to buy automatic cars and rental companies are reluctant to keep a large automatic fleet, which are hard to quickly sell in the used car market.

If you need absolutely an automatic car, you have a much better chance if you rent at the major locations in Florence (Florence airport or Downtown) where there are large numbers of American renters to justify the availability of those cars.

The drive from Florence to Cortona is easy, as it is virtually all on a freeway. As far as returning your car, I'm pretty sure you can return it at any location, regardless if you rent an automatic or not. Only Hertz is in Orvieto however. Not sure where you are going next, but if after Cortona you go to Rome, you could return it in Rome, where all companies are present and with many offices, including some very easy to reach from the freeway.

Pick up Florence airport.

If you don't need the car in Orvieto, return in Chiusi. Or drop in Rome.

Look at Auto Europe or kemwel