It occupied Alsace-Lorraine because they were primarily German speaking territories. The entire purpose of the Prussian goal to form a German nation (at least for PR purposes) was to unite all German people under one banner and yadda yadda. A non negligible French minority chose to leave (about 11 or 12% if I recall), as they were permitted by the Treaty, but a sizable French minority remained.

So that was the public reason, and a very good reason at that. What are some of the behind the book reasons? Well, firstly, putting those nasty Bavarians in their place. The issue of Bavarian independence was a fierce one, one that persisted even after WWI when they seceded in the aftermath of Versailles. They had spent at this point over 2 generations as a strongly centralized, independent state with a distinct Catholic identity (opposed to the Protestant of the Northern German states). They spent a large amount of this time having their independence guaranteed by the so called German Confederation, headed by Austria, which was a notably decentralized entity.

Once Austria was soundly beaten, Russia was threatened into submission, and Britain stopped caring, France was the last vestige of hope for Bavarian freedom. Catholic France, mind you. Staunchly Catholic France. In fact, Catholic sentiment was so strong in Bavaria many who lived there felt a stronger association with the French than their German counterparts in the North. A medieval form of policy, Ultrmontanism, 'political Catholicism', was revived in 1860's Bavaria even and strong nationalist bodies were elected. This feeling of separatism was so strong that Prussia incorporated just about everywhere else directly under their clout as 'Germany' -- Bavaria was allowed to maintain its own military command, its own uniforms, its own railroads, etc. up until the Weimar Republic.

So, with Bavaria bordering France, the seizure of Alsace-Lorraine becomes kind of clear. It puts Prussian controlled land all around Bavarian control, and Bavaria loses their only border to their only ally left. It was sort of the last knife to bring down the beast of Bavarian independence -- it isolated them almost wholly and forced them to capitulate to German unification.

A second note of particular importance to the military staffs too was the former borders gave the French a natural defensive position on the Rhine along with dense forests and mountains. With the seizure of Alsace-Lorraine, the French no longer had a suitable launching point to attack into Germany, and Germany had essentially a buffer state between France and the Rhine.