There are a few things called Luxembourg and that might create some confusion:
- A small country located at the corner between Belgium, France, and Germany. The color of the flag is more red than orange. It was ruled by the House of Orange between 1815 and 1890 and the shape of the flag inspired by that of the Netherlands but I don't think it ever included the color orange, unlike the Dutch flag.
- The capital of this country, sometimes called “Luxembourg City” or “Luxembourg-Ville” (also the name of the main train station I think).
- The Belgian Province de Luxembourg, a region of Belgium located just next to the country named in point 1.
Now, Schengen is a village on the Luxembourgish side of the border tri-point between Luxembourg, France, and Germany. The agreement itself was signed on a riverboat, so as to symbolically be “on the border” without knowing exactly in which country (although for legal purpose, it's considered to be Schengen and Luxembourg is the depositary of the original treaty). The boat, called “Princesse Marie-Astrid”, still does cruises on the Moselle river.
Finally, Schengen is very small, I don't think the area around it was ever known as “Schengen area” in any of the local languages. What's now called “Schengen area” is typically the whole 20+ country strong border-free area.