With respect to Paris, it is really difficult to see much, if you have only one day and are going down from Le Havre. You could take a train, then a bus tour from inside Paris , just to get a flavor. I actually think a better bet would be to go to Normandy, taking a train to Caen, then hiring a taxi driver to take you through Normandy to a couple of the towns and the D-Day beaches, including the American Cemetery at Omaha Beach, which is easily one of the most moving places I have ever been. Also, Caen has an amazing Holocaust museum, which is worth a 1-2 hour visit. If you go to Normandy, be sure to go to Arromanches, which has a fantastic museum showing you the D-Day landing operation, including a most fascinating coded map used to deceive the Germans about the landing plans. I am not a big war historian, but I was really captivated by it.
The other excursions I would recommend from Le Havre would be Mont St. Michel or Giverny. Both very do-able from Le Havre.
I would also recommend Brugges, though not Brussels.
If you do decide to go to Paris, I recommend one more thing to help. I would engage a private tour guide. The advantage of the tour guide is that you can get the exact itinerary you want, and you can jump the lines at pretty much all the museums and attraction which give special privileges with tour guides. You might be able to have the guide meet your train and then use taxis to go from place to place.