Ghent to Luxembourg to Paris?

You won't find any direct trains from Ghent to Luxembourg, you'll have to change in Brussels. The railway trip is slow by current European standards but there's some nice scenery around the Ardennes.

Luxembourg isn't that worthwhile as a tourist destination though - if you want to do a loop back to Paris I would recommend Nancy (if you are into art nouveau) or Strasbourg (if you prefer a medieval or early modern atmosphere).

Consider stopping in Strasbourg and/or Colmar on your way to Paris instead.

I have done the trip from Gent to Brussel many times by train. Gent is served by two stations, the main one is St Pieters, but both stations provide trains to Brussel. The ones from St Pieters tend to be more frequent and faster.

The train from Brussel to Luxembourg is frequent and direct, and is - as mentioned by Philip - not a bullet train. It tends to be operated by slightly older equipment and never exceeds about 160 km/hr (100 mph). The scenery is pretty nice.

Luxembourg operates a very integrated transport system, with trains going down several branches and supplemented by buses going to most cities and towns linked by connecting buses. Most CFL (Luxembourg trains) are modern double deckers which give nice views. The CFL buses are almost all modern air conditioned single decker front entry buses which are closer to coaches than buses.

Luxembourg City is easily walkable and lifts are provided to change levels in several places.

Luxembourg to Paris is a route I never have done. You would take a train from Luxembourg due south to Metz in France which I understand is a nice city. You then get the train into Paris. I haven't looked it up but I think that most high speed TGV Est trains to and from Strasbourg would bypass Metz, but there are certainly trains.

There are also through TGV Est services from Luxembourg to Paris.

cool - that's an improvement, big style. Thanks, Philip.

Train service may not be as direct or frequent as you expect to some of that area and even a map doesn't tell the whole story. To see real connection choices between towns, How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

I also think that Luxembourg is missable, but it's certainly not a mistake to visit there. I would say that Trier, Germany is also worth a day. Because it is so well-connected to Brussels, I urge you to consider Cologne, Germany if you haven't been there. It's good for four days even if you don't leave the city limits.

I noticed a college-sponsored (that is, escorted) tour with the title New Museums of Northern France, which certainly interests me, but wouldn't interest everyone. And you didn't say how much driving you'd be willing to do. Here is a link to the Smith College travel sponsor, but I HAVE NOT been on this trip. I'm posting for the museum list. For when the link disappears in the future, the cities seem to be Lille, Metz, Nancy, Reims, and Paris. I have been to the Lille Palais de Beaux Arts, and it is both worth a visit and roughly on your route.

http://alumnae.smith.edu/travel/smith-travel/2015-trips/new-museums-of-northern-france/