I was just looking over ADR's FCO website (Aeroporti di Roma) and saw under their "To and From Fiumicino" page: Car Sharing
Here's the link (but keep in mind that ADR often rearranges its website rendering links invalid, so if this doesn't work, start from ADR's homepage):
Car sharing - Aeroporti di Roma
Here's a cut and paste:
With Car Sharing it’s now even easier to travel from the airport to the centre of Rome and vice versa! Pick up your car from the airport and leave it in a different place at the end of the route, available for other people.
Car Sharing is an alternative but also a beneficial opportunity for sustainable passenger transport. Forty stalls dedicated to Fiat 500s by Enjoy and Smart Fortwos by Car2go are available at Fiumicino.
To benefit from the service just download the Enjoy or Car2go App and you pick up your car directly from the Short Stay car park at Terminal 1.
I for one would never use this (I'd be scared silly to drive into Rome). But I'm curious if any of you have heard of this, and have used these cars?!
Here are the links to the companies mentioned:
Enjoy
Car2Go