Best European flight connection

There are likely many many options. Plug your home airport into Google and see what comes up, then we can help you evaluate them. You have to determine if it works better for you to change in a European city and fly into Florence, or fly to Pisa or Rome and take a short train ride to Florence from there (I'd opt for the latter).
We all have airports we avoid for various reasons--I try to avoid London, Paris, Frankfurt.

Florence Airport has a relatively short runway. This means that the largest airplanes that can land there right now are planes the size of the Airbus A320NEO and the Boeing 737. In general these type of single aisle planes are not used for transatlantic flights. This is why you won’t find direct flights from the US to Florence Airport.

Very interesting and helpful explanation.

We did a tour of Tuscany and Umbria earlier this year. The tour started in Siena.
I looked at flying into Florence, but it would have required an additional change of flights in Europe, so we flew into Rome and took the train to Florence, changed trains to go to Siena.
The Rome-Florence train only took about an hour and a half, it was high speed.

We have always been happy flying Delta to Amsterdam and then KLM to Florence.

I've had smooth and not so smooth connections via LHR (London), CDG (Paris), FRA (Frankfurt) and (AMS) Amsterdam from my home airport to FLR. I make my flight decisions based first on timing; outbound departure time and amount of layover time. I prefer afternoon to early evening departure with minimum 2.5 hour layover and I'll make sure my seats are far forward within the main cabin.

From RDU....

American flies to London Heathrow;

Lufthansa flies to Frankfurt;

Air France flies to Paris.

All of the above are nonstop.

From each you can connect to a flight to Florence. Probably on one ticket.

There are also flights from RDU to Reykjavik on Icelandair and starting next April flights to Dublin on Aer Lingus. But they don't offer easy connections to Florence.

Definitely fly to Rome (or Milan, if there's a direct flight from RDU) and train to Florence. You might even get lucky and be able to go to Florence from FCO and not have to transfer to Termini.

Just our opinion, but we prefer flying through Amsterdam. Paris is our next preference.

We had a direct flight from Atlanta to Rome.
Having to break it up transferring in Amsterdam or Paris adds several hours to your travel. We got to Florence quicker flying into Rome then taking the train to Florence.