Is this a stand-alone trip to France, meaning that you will be arriving on April 11 after an overnight flight from the US or Canada? Some folks find their arrival day is a zombified blur and not worth much for sightseeing purposes. You're young and may do better. It's definitely best to be outside on your arrival day, which fits well with your preferences. If my assumption about the trip is correct, you have only eight full days to play with plus some hours on April 11. I can't imagine going to the huge city of Paris plus two other destinations in that amount of time.
Assuming you fly back to North America on April 20, there probably won't be time for much sightseeing that day because your airline will suggest that you be at the airport at least 3 hours before your flight is scheduled to depart.
If you travel to Nice from elsewhere in France on April 14 and leave on April 17, you'll have just two full days and a few hours in Nice. I wouldn't do that; most people want to see some of the attractive coastal and/or hill towns while they're in the area. And the trip to Nice could be quite long; that obviously depends on where you're traveling from.
Any day when you shift hotels/cities is a day half-gone, at best. You'll lose more time than that on April 17 when you relocate from Nice to Paris. If you're willing to get on a 6:57 AM train from Nice (I wouldn't be doing that on a vacation), you can be in Paris at 1:53 PM. A saner departure time of 8:23 AM gets you to Paris at 3:23 PM. As you can see, once you are settled into your hotel and oriented, you have only a few hours left pm that day. So you're giving yourselves just two full days and some hours for Paris at the end of the trip.
So I think you're setting yourselves up for seriously inadequate time in both Nice and Paris, plus a lot of travel time. I'd rethink this trip completely. I enjoyed Nice and surroundings a lot, but I'd suggest dropping that area and focusing on Paris and one area not too far away. Alternatively, plan on Nice and Paris but alter the schedule so you either begin or end in Nice and fly into or out of the Nice airport.
Edited to add: You've listed your dates in the original post in a way that suggests you have more time than you do. You show your travel days as if they give you time in both the departure city and the arrival city. That can lead you down the garden path as well as confuse responders. This is what I think you really have:
April 11: Arrive in City A after overnight flight (3 nights)
April 14: Travel to Nice (3 nights)
April 17: Train to Paris, 6 to 8 hours (3 nights)
April 20: Fly home
The conventional wisdom on this board (for a very good reason) is that 3 nights somewhere gives you just 2 days.