Itinerary help: Rome, maybe Florence, then a couple days in Paris: 2 weeks

If both Pompeii and Herculaneum are MUSTS, then you should plan to spend ( at least) 2 nights in Sorrento.

Trying to do both in a day trip from Rome would be folly. The survivors would be really grumpy the rest of the trip

"2 weeks"-- how many nights in Europe is that?
"..few days in Paris" not sure everyone defines 'few' the same way

If you can provide more specifics, you improve your odds of useful answers

Focus on Italy, save Paris for another trip.Rome and Sorrento will give you access to what you want to see. You do not want to travel to Pompeii and Heraculaneum from Rome, too far. Thus Sorrento as it is much closer to those antiquities.
Airport to Rome has a taxi flat rate. Use a taxi.
Getting around Rome? We have always walked plus an occasional taxi.
Hotels? What area do you want to stay in? Between Piazza Navona and Pantheon is Palazzo Navona, modern hip hotel set inside antique palazzo. Best area for seeing antiquities on foot. Maybe you want a pool? Farther out, GrandHotel Parco Principi., above Galleria Borghese.
It would be wonderful to include Florence too.

No, you do not want to stay in Rome and take day trips to Pompeii and Herculaneum. Stay in Sorrento or Naples, Naples would require less travel time if going to Florence from the Campania region.
While in Rome you’ll walk to most places but I recommend taking a taxi since there at least three of you, even from the airport.

For first trip always recommend the big 3…fly into Venice and out of Rome, spending three nights between in Florence. Although many don’t recommend it, we did a day trip to Sorrento-Positano-Pompeii through See Amalfi Coast with a private car and driver. You catch an early train to Naples where the driver meets you. We were back in Rome in time for dinner. They offer tours that include Pompeii and Herculaneum as well. It was a full day for sure but we saw a lot in a short amount of time.

Looks like you haven't made any reservations yet, so that's good. If Pompeii and Herculaneum are must do, then see if you can fly into Naples. If not, then go directly on arrival in Rome to Sorrento for at least 2 nights, preferably 3. Then train back to Rome for 3-4 nights. Proceed by train to Florence for 3 nights, then fly to Paris for the remainder of your trip. This all assumes you have the full 2 weeks in Europe. But if it includes your transatlantic flight days, then skip either Florence or Paris.

I find rushing to punch a ticket makes for an unsatisfying trip. With only two weeks, do Italy -- mix up big cities and smaller places -- do France/Paris on another trip. I'd spend 3 nights in Venice and mostly wander around, 4 nights in Rome and Florence and then a couple of nights in Sorento to do Pompeii and Herculaneum -- and try to factor in some time for Siena -- maybe as a day trip from Florence and do 5 nights there to accommodate that side trip.

Fly into Venice (of if you must round trip into Rome then go immediately by train to Venice) then do FLorence/Siena then head for Sorento and the ruins and then finish with 4 nights in Rome to fly home.

My personal preferences differ from those of others on this forum. I have done Pompei(but not Herculaneum) twice as a day trip from Rome. Once on a long day bus tour that included the Amalfi Coast drive, one as just a visit to Pompei with Enjoy Rome. I am not a fan of Venice but Florence is my #1 favorite city. If you decide to go to Florence, you should be able to fly directly to Paris from the airport in Florence (or at least you could do it pre-Covid). I'm not a big Paris fan, but would always choose it over Venice.

I love Venice but the OP didn't mention it and seems to have enough already in the plan. I agree that Pompeii/Herculaneum would be a bad day trip from Rome. Sorrento or Naples would be a better base for these. And I agree that with three or four people taxis make the most sense between airports and hotels.

If Paris is a must, but Florence isn't, then go to Paris. Fly into Rome and home from Paris. If Paris isn't a must for this trip, then I agree with others that Florence would be a better use of your limited time. If you're "not stuck on exact number" of days, then give the trip as many days as you can afford time- and cost-wise. Transatlantic flights are unpleasant (putting it mildly), get the most Europe you can for those flights.

Two weeks isn't a lot of time. On our first trip to Italy, we had 18 nights and that we spread across Rome, Florence, Cinque Terre, Venice and ended with four nights in Paris. We took the night train from Venice to Paris which was an interesting experience. It seems people either love or hate sleeper trains. For the two of us, it ticked both the transportation and lodging boxes. We enjoyed it but I would have upgraded to a better sleeper compartment. It got into the station in the early morning and shook up our sleep patterns but gave us a full day in Paris.

In retrospect, was it worth it? Yes and no. It goes back to your motivation. Rationally, we should have canned Paris and stayed in Italy. However, one of the things that sustained me during COVID was the memory that I had been to Paris. For two weeks and with teens, I'd pick one or the other.