DB operate an express bus Saarbrücken-Luxembourg, and there's a variety of rail routes across the hills of the Southern Pfalz to connect.
Alternatively, Karlsruhe-Strasbourg-Metz-Lux. by TGV but limited services.
Or an all-rail route Karlsruhe-Saarbrücken-Trier-Lux.
I think times via Strasbourg change soon (July?) with the extension of LGV Est.
There are certainly new Luxembourg-Metz-Strasbourg TGVs (to Lyon and beyond).
Alternatively, you can travel by DB trains via Koblenz and the Moselle valley via Trier.
The all-rail route via Trier can be used with a Rheinland-Pfalz Ticket "+Luxembourg "(new to me!) @ 30 for one, 35 for two...50 for 5.
Valid on all regional trains from 0900 and at weekends over a vast area, book on the day, go when you want. As there are hardly any IC type services on the route, you're not missing out on a quicker journey (though it would be a bit slow going round via the Rhine Valley).
The rail and bus route starts at 29 per person, booked in advance for a specific service, so I can't see any advantage in using it.
If you do not mind buses and do it only one way-then there are various LUX buses from some stations along the Trier-Moselbahn-toward Apach into LUX-just pay driver 2 eur for the 2 hr single-connect anywhere into LUX.
Last year in the local summer school Hols the RhPf ticket was valid any day alltime-thus mo/fr also before 9.00.
For a while DB also offered what was in fact the LUX Airportbus from FRA-via HAHN (Ryan)airport run as flibco as a DB-IC-route, I do not know if that is still so-this may be at appropriate times be the fastest connection-just 1 change at FRA HBF.