train vs. plane in Italy?

I assume you do not mean fly Venice to Rome? The train is obviously the choice there. Rome to Paris would be a very good flight option, and my preference if you need to get there in less than a day. Just watch for taxes and added fees, especially baggage fees, that can make a cheap flight cost a small fortune.

My dd and I flew from Paris to Rome last summer, I had looked at the trian, but it was expensive.
We flew Vueling and paid 80 euros one way. I noticed that a few months after I booked prices went up.
It was not really a hassle at all. Flights inside Europe do not require a three hour check in,, I think it was one hour, but of course I was there 2 hours ahead just to be careful .

There were no hidden luggage fees.They are written out plainly on website, read carefully, no matter who you book with. You get one free carry on,( plus purse) and you can pay to check a bag in, we checked one in. It is very clear that you must check bags of certain size, and that if you try to take a bag that is too big on board you will have to have it "gate checked" and that is more expensive. I think it was 5 euros a bag if you book and pay in advance, 15 euros to gate check.

I would take the train from Venice to Rome, but I would probably fly from Rome to Paris.

Typically, if the train ride is 5 hours or less, I always choose the train ... even when it is more expensive. Train stations are usually conveniently located in the center of town. Trains are also more likely to arrive on time and the seats are far more comfortable.

When comparing price and time on rail vs flight, remember to account for the waiting time at the airport and the time and cost of getting to and from the airports. The airlines will generally show fees on their websites. Budget airlines are more likely to have the added fees.

I agree with Laura, I'd take the train from Venice to Rome, and fly from Rome to Paris.
The trains in Italy are excellent, just watch out for strikes!