This is a pretty decent schedule.

To pick up days, my suggestion would be to take 1 day from Amsterdam and 1 from Paris. That would allow you to visit someplace in between them for 2 nights, like Brugge, Ghent or Antwerp, or add days in Provence, somewhere other than Nice, perhaps. You could also take 1 from Rome, too, I suppose, but then again it is Rome. With what you have planned form the AC, Capri taking an entire day, you will probably want those 4 days.

Prague-Amsterdam is long enough for a flight to compete with rail, but Amsterdam - Paris should really be done by train. It is only a 3:19 minute trip.

Paris - Nice is also suited better for rail travel, clocking in at about 5:40 minutes, with some scenery and the thrill of traveling at over 200 mph, which creates it's own scenery.

Nice- Florence is probably a flying route at 7:30 for the train, unless someone can vouch for some interesting scenery. From Florence, you want to be back on the train.

I would probably start in Prague, then Amsterdam. From Amsterdam, a cheap budget flight (maybe Transavia?) to Nice. Train to Paris next. Cheap flight from Paris Orly (Easy Jet) to either Venice or Rome to finish the trip.

Look at budget flights on whichbudget.com or skyscanner.com.

Are your travel days included in the numbers reflected after each city? If yes, you don't have 4 days in Amsterdam, 6 days in Paris, 2 days in Nice, etc. By the time you've packed and left one hotel, traveled to the next city, and checked into the hotel there, you've lost a half day or more. You should investigate all your travel times and plot this itinerary out in real time before you consider taking days away here or there, adding destinations, etc.

Investigate flying Nice-Florence in particular. I'm not sure there are direct flights between the two cities, and it could end up taking several hours. Nice-Pisa may have better options, and there is direct train service from the Pisa airport to Florence. If it were my trip, I'd skip Nice altogether and fly Paris-Florence. I'd want more time in Florence to provide the option of seeing a Tuscan town or two.