Luxemburg was not a German state, exactly. It was considered a part of the German Confederation by treaty, but later treaties further defined and expanded its enforced independence and semi-neutrality. By the time the Franco-Prussian war started both sides specifically avoided entering Luxemburg's territory as it was considered neutral. Furthermore Luxemburg remained in a personal union with the Dutch monarch in the Netherlands until 1890 and as such it was already counted in the Dutch sphere of influence such as it was.

Luxembourg used to belong both to the German Confederation and to the German Zollverein but it was also in a personal union (ruled by the same monarch) with the Netherlands. In 1815 it was declared a German Bundesfestung, a border city to be manned with united German troops flying the yellow Black Eagle banner.

After the German Confederation was replaced with the North German Confederation in 1866 Prussian troops entered Luxembourg and Napoleon III promptly bought it from William III of the Netherlands which resulted in the Luxembourg Crisis: Bismarck was ready to declare war on France if French troops would enter Luxembourg.

It was to be resolved in the London Conference of 1867. Prussian troops had to leave Luxembourg within 15 years but the agreement for sale between the king of the Netherlands and the emperor of France was as well declared null and void. Russia, Britain, Austria, France and Prussia agreed to indefinately warrant the independence of Luxembourg if it would also remain neutral in future wars. For the time being it was ruled by the king of the Netherlands.

The personal union between NL and L ended in 1890 since William III had no male successors. The Netherlands were inherited by queen Wilhelmina and Luxembourg fell to prince Adolph of Nassau who previously was dethroned by the Prussians when they annexed the Duchy of Nassau in 1866.

Just a note of correction: Liechtenstein is another minor German state (having belonged to the HRE, the Rheinbund and the German Confederation) that didn't participate in unification.

The Fortress of Luxembourg was destroyed starting in 1867 and ending in 1883. Its destruction was required by the 1867 London Treaty that also disbanded the old German Confederation and settled the paperwork for the Austro-Prussian War.

Now, more to the point, these were feakin' huge fortifications built over many years at a very crucial point. If the French held it, they could attack into the German heartland. If the Germans held it, the could go into the France or the Low Countries (or strike east) unconcerned about a French attack. If a Great Power held the fortresses, it would lead to a foolish adventurism.

So all the powers agreed to stop trying to buy or otherwise take over Luxembourg and they agreed to tearing down all the walls and towers the girded 'round the the place. This way nobody had a threatening advantage.

So it was decided to make the place a neutral zone.