Pisa to CT is just over an hour by fast train,via La Spezia.
CT to Venice...a lot longer,something like 6 hours.That is basically a day of your trip gone....so you would need to expand Venice to 3 nights I guess.
Venice-Rome is about 3.5 hours.
With your timeframe,personally I'd drop the CT and just visit Paris,Venice and Rome.That can be done all by train if you want,or with budget flights between Paris and Venice.It gives you enough time to move between places and to see Venice,as well as the other two cities.

