Luxembourg is a good option. D-Ticket is valid until the border point and public transportation is free in the country. Then 8€ for a TGV reservation.

It could be faster (but more expensive) via Aachen/Belgium. You need a ticket between Aachen and the border (Aachen Süd (Gr)) on a regional train. Or between Aachen and Hergenrath -> whichever is cheaper.

In addition a 27€ Eurostar reservation from Brussels.

Where please is the Border to Luxemburg ?

and „Aachen Süd“ ist der Grenzbahnhof zu Belgien ?

Yes Aachen Süd is the border point. There are no stations so it's a virtual border.

You can get such ticket at a counter or you buy an Aachen - Hergenrath ticket online (easier) here: https://www.b-europe.com/EN (4.70€).

About Luxembourg you'll board the RE11 in Koblenz. Igel (Gr) is the border point, D-Ticket is valid up to there and afterwards transportation is free.

For example:

Düsseldorf Hbf → Luxembourg
Wed 10.07.2024

RE 5 (28511)
To Koblenz Hbf
From 09:58 Düsseldorf Hbf, platform 16
To 11:42 Koblenz Hbf, platform 2

RE 11 (5112) / RE 11 (5112)
To Luxembourg
From 12:06 Koblenz Hbf, platform 9
To 14:23 Luxembourg, platform 11

Little break and then direct TGV at 16:10 (8€).

2 side notes depending on travel date:

- there are works around Düsseldorf after mid-July. Trains will run at different times. Some trains (incl. RE5) don't stop at Düsseldorf Hbf.

- there are works between Luxembourg and Bettembourg after. You'll likely take a replacement bus to Thionville.

Obviously get ready for the usual Ruhr delays...