connection time worry

Are the two flights on a single ticket?

It sounds like one ticket so I would not worry as there are 6 flights after that operated by United alliance partner Lufthansa and they will just put you on the next one with space.
You paid for a ticket with such a short connection because it was cheaper and now you are worried about your decision.

If it is one ticket. You are fine. Most international flight tends to be on time. You will have to go through immigration and probably security again for the second flight. If running tight look around. There are generally special lines for short connections.

This could be close, but the airline planned it so you could make it. USA to EU flights are rarely late unless there is an unusally long delay in USA take off. Go directly to the FRA departure gate, then go shopping if there is any time left.

yes they are on one ticket.

You are good to go. If for some reason you miss the connect, they will have to take care of you. We are missed some tight connections over the years so that adds a little inconvenience waiting for the next flight.

We do not have our seat selection yet

Are you on a Basic Economy ticket where seats are assigned at the gate? If not, I would try to go ahead and grab seats as close to the front as you can. As noted above, the worst that will happen is that you get bumped to a later flight if you can't make the connection.

I once booked a 45-min connection early morning at CDG (Paris) because the ticket was dirt cheap. Immediately after purchase, the connection time went down to 40 minutes, below the "minimum connection time" of 45 min for the airport. I called Delta and the guy on the phone said, "Yeah, you'll make it." So, I kept the itinerary. My incoming plane arrived 15 minutes late. I walked fast to the gate for my flight to Budapest and made the connection because that flight was delayed about 15-20 minutes.

Hopefully this tight connection saved you a bunch of money, hopefully your first flight will land on time, and hopefully seats will be available on the next flight to Rome if needed. This connection time would make me nervous and freak out my wife, but chances are you'll be OK. If not, and you spend more time than you need to in Frankfurt, do some shopping with the money you saved on the ticket. ;-)

Glad you are on one itinerary.

That said, if your flight departs BOS late and you miss your connection in FRA, you may or may not be automatically moved to the next flight of the day to FCO so go to the Lufthansa counter (I'm assuming you'll be flying Lufthansa as it's a UA partner) and make sure you're on the next available flight with seats. You may be seated separately. Even if you do make your flight, you might be seated separately on your FRA - FCO flight anyway unless you contact them to select seats; they may charge you.

Dave, you make me feel better about my 1h 40 min connection at CDG in April. Looking back, I'm really not sure why I thought booking that was a good idea. And, it happens on Good Friday, so I'm not sure passport control and what-not are fully staffed. Eek!