The big 2024 timetable change happens on 10th December (European-wide). Timetables will be published around October.

Train times should not change much so you can check next week's timetable to get an idea. Use a reliable planner like bahn.com or DB Navigator app.

Honestly don't try to drive in major cities like Paris, Amsterdam or Brussels. You'll lose hours in traffic while the train leaves you right in the city center.

Now the second point is : passes or regular tickets ? The pass would give you a lot of flexibility but remember that reservations are mandatory on high-speed trains in France. Book a few days in advance, especially around Christmas.

If you only want to visit the locations mentioned above than I don’t thing a pass will be good value. How old are the children. Under 12 they usually travel for free per paying adult (or very cheap)

Public transport in Luxemburg is free, in Belgium it’s quite cheap when you juggle a bit with your tickets (e.g. weekend ticket at 50% discount, some special passes). If you avoid Thalys (soon Eurostar red) to Amsterdam it’s gonna be very okay price wise.

You have TGVs from Luxemburg to Paris, which don’t have to be that expensive when bought in advance.

The only thing you have to pay attention for is the fully booked trains around Christmas, especially for the TGV to Paris.

Belgian and Dutch domestic trains can’t sell out, as they’re very frequent and don’t have reservations

Long distance trains (TGVs) will be very, very busy as most people will make their way to their family for Christmas and will sell out some days/weeks in advance. Avoid travelling at 22-23-(24)-(25)-26-27 December, or try to book TGV tickets Luxemburg-Paris soon, they can be bought from 4 October.