Were you planning to do Hampton Court on the day you head to Paris? If that is the case I think it will be too rushed.
I love Hampton Court, but really it takes me at least 3/4 of a day including getting from my hotel to/from the train station, walking to/from the Hampton Court station to the entrance, then seeing the Palace. And I've never spent much time in the gardens because I always seem to be there on a rainy day, lol!
With your short time, I would probably skip Hampton Court this time unless it is a must for someone in your party.
Incidentally, I feel the same about taking a day out of Paris to see Versailles!