Travel by train from Rome to Paris

That is the route. If the high speed train arrives to Turin on time, 19 minutes should be sufficient to transfer, although I'd prefer at least 30 minutes just in case.
Train statistics: 40% of trains arrive on time or early. 60% are not on time, but the average delay of those that are not, is less than 10 minutes.

19 minutes is a good connection time. If the first train is a little late, they may hold the connecting train to Paris, but not for long. Assuming it is a single ticket, you could get on the next train to Paris, but that is not until 6 hours later. Time enough to have a look around Turin.

The Freccia trains run consistently to schedule except in unusual circumstances. The Porta Susa station has only 6 platforms, so getting from one to another should only take a couple of minutes.

Thanks ... So, the next question is whether it is worth taking a chance.
If the train is indeed late and the connection cannot be taken, would the bookings on the Paris train be automatically moved to the next train without charges.

It is so much easier to take a budget European airline on that route. Distances are greater on the ground than most people realize.

Train tickets with reserved seats cannot simply be transferred, you need to go to a ticket agent and get a new ticket (if your incoming train is late enough for a missed connection, there will be no charge; but if you have a super-economy or economy ticket and you miss the connection because you didn't get to the second train quickly enough, you will have to pay for all or part of a new ticket.

Better to fly.

Rome to Paris is loooong on the train. I would fly (my in-laws live in Turin, and I do that portion regularly by train).

Note that the next (and only) direct Turin-Paris train departs 6 hours later. Out of the 10-hour train ride, only about 2 hours will have mountain scenery. The rest is along busy transit corridors through average countryside.

We have done Roma to Paris (and return) three times. Only once did we do the entire trip in one day and we agreed: Never again! It was 14 hours total and we were very tired of the train the last three hours from Milano to Roma. Can you go to Torino (a lovely city) and spend a night or two, then go on to Paris by train?

I will always choose the train over flying if at all possible!