If you draw your route onto a map you will get some idea of the routings and distances. 
Q1 is how are you getting to Paris?
Q2 is how many days holiday and how long do you want to spend at each stop?

Q3 is how long do you want to travel each day?

I would miss Paris as a starting point and head for Brussels. From Brussels you get the ICE to Cologne, then onward to Berlin, otherwise you have an expensive or convoluted train routing to Berlin. 

From Berlin consider staying in Nuremberg (direct ICE from Berlin) - then a couple of regional day trips to Bavarian towns such as Bamberg and Regensberg.(or a trip to Munich).

Then Nuremberg via Munich and Brenner pass into Italy - Verona, Bologna and Venice are all potential stops. The high speed line from Verona is a direct service to Florence, Rome, Naples and Salerno. There will also be regional services between these stations.

I would allow at least 10 days to get to Salerno and stay in Berlin, Nuremberg, Bologna or Venice, then I leave it to you how you plan the Italian Cities. If you take any less you will not experience the culture of these cities. You need to stay at least 2 nights (arrive, tourist day, depart).


 

From Berlin the best way is to travel via Prague. Via Bavaria is very long, you could take an ICE to Munich and from them RJX to Budapest via Vienna. But it should be longer. 

Of course it depends how long you'd like to stay en route, what you'd like to see and how long a single train trip may be. Even in Bavaria. Mountains? Lakes? Castles? Small town? Big City?

There are some really scenic ways to go from Bavaria to Budapest. But the scenic parts are mainly when going through Austria. And it will take much longer than the direct way. 

There are also possibilities to go by boat at different places along the route if this may be of any interest. 

Maybe you should specify what you are interested in to get specific ideas. 

We don't have to go through Bavaria, that was just an idea.  Quite happy to explore other routes and maybe a town would be good rather than another big city.  We would probably stay 2-3 nights depending on what there is to do.  I would just like to experience some scenic routes on the train so the Alps would be good too.

Either you catch a direct Eurocity from Berlin through Dresden, Prague, Bratislava to Budapest (a very long train day with nice views between Dresden - Prague and from Szob to Budapest) with a nice dinning carriage

or you catch a direct Nighttrain from Berlin to Budapest :) 

via Bavaria would be a detour you may go via Vienna 
From Berlin you have daily a direct ICE to Vienna (via Nürnberg,Passau,Linz) , a Nightjet Berlin to Vienna & a Night Intercity (that i dont recommend to use)