I am thinking of changing my plans from taking a train to Florence

Recheck luggage, Go thru security, Find your new gate and board

Not sure if easier but possibly riskier
What if your first flight is late and you miss connection?

Then from FLR you’ll need to get to the city -tram or taxi

The only airline that flies to FLR (4 flights a day) is ITA Airways.
If you fly with ITA or a partner (like Delta) to Rome, then you can see if they will check it through.
The four ITA flights from FCO to FLR currently depart at 9:15am, 1:55pm, 6pm, 9:45pm
After the end of September I think ITA reduces the flights to 3 a day.

I'm not convinced flying will be easier. A train has more space to move around which seems like a good thing if you have a broken arm,

Are you committed to flying to Rome?

It appears United/Lufthansa have 1 stop Denver-Florence flights ( either Munich or Frankfurt)

A DIY 2 ticket booking US-Rome and Rome- Florence is an invitation for high drama and possibly a missed connection.

What time of year will the trip be?
Is weather likely to be adverse?

If you must add on the Rome-Florence flight, anything less than 4 hours looks very scary.

My $0.02