We're looking for a car hire

If you are only looking to go from "A" to "B" by taxi I would suggest you use the licensed taxi's out front. There are loads of them lined up and queues when we were last there... Lots of all white licenced taxis with registration clearly marked and I believe fixed price from the airport to city centre. Look on the airport site, last time they even had a price list on there...

Taxi fares listedSteve is right, if you just want to get into Rome take a taxi or the Leonardo Express train. On the ADR site they list the taxi fares and yes the comune of Roma controls and sets the fares:https://www.adr.it/web/aeroporti-di-roma-en-/pax-fco-taxi

Agree with the train which i have used and  also you have the Terravision bus service into Rome centre,if on a budget both considerably cheaper than the taxis.