The str8forward route from AMS to Lux is daft easy: only 1 change from hourly train to same: at Brussel Noord-unless you have specified maybe a special scenic route? or maybe just on that day there are works or whatever going on. OR via Maastricht-LUik (LIege)=change there, but connections not very good).
BTW; IF you proceed from LUx (where all transit is free) there is no need at all to go via Paris to go south-TGV toward Marseille-Nice also start from Strasbourg (much less though) . The se planners however often have a tendency to send people via expensive extra payment routes.
The ONLY routes were a RES on TER is-sometimes-needed are the Nomad trains from Paris to Normandie=far away from this routing.
Note however that PACA region (around Marseille-Nice) has STOPped accepting passes since 1/7!!!
All this trains is not possible to reserve a seat. I am not sure for the TER in France, because every Territory in France has other rules for regional trains like TER.
Why are they all greyed out? It was like that from Germany to Amsterdam and the train was crowded but it worked out. However, I asked a girl in the DB Reizecentrum in Hamburg and she said that it was harder to go without reservations in france, and I’ve heard the same thing from a friend. I don’t wanna miss my booked train to Nice so therefore I want to be sure.
All of those trains are unreserved and you are free to use with a pass.