Be careful about French trains if you do not speak French well ! I got lost a lot. (I speak French now, but I found the train system scary).
Otherwise, it depends on what you like... You could spend 3 days in the Louvre alone. Paris is a huge city, and three days is not nearly enough to see even the highlights.
If you want a day trip, Versailles is probably the easiest/most interesting thing to see (if you can make it, my favourite place to visit iniFrance is Normandy - I really enjoyed the tour I did there, but it's a bit far... also, I'm a war history nerd, so that would be really high on my travel priority list).
Walking around Notre Dame, grabbing a coffee, going into the book store (it's on the right of Notre Dame, across the bridge - tiny, and sort of hard to miss), eating good food, and then heading down to check out Place de Republique would also be high on my list of fun in Paris...
But, be sure to budget time and money to eat out ! The food in France is amazing, and not to be missed.