My impression is that that lesson was NOT drawn at the time by the German A-listers, and especially not by Bismark - the AAA-list genius behind both this victory, and Germany's long process of unification. Bismark was very public, both before and after the Fraco-Prussian War, in his general opposition to European wars. Especially larger or longer wars. And he was very opposed to risking Germany getting caught in a two-front war.

But then Germany's Kaiser Wilhelm I got old and died, and was soon succeeded by his grandson, Wilhelm II - who didn't like Bismark's cautious foreign policy. Wilhelm II wanted vigorous & rapid expansion, to enlarge Germany's (and his) place in the sun. Bismark, who was getting a bit old & unsteady himself, was replaced in 1890 with a new German Chancellor, more to the young Kaiser's liking.

Note that both WWI and WWII stuck Germany in large, long, two-front European wars. And that Germany got into WWI under the same Kaiser (Wilhelm II) who had dumped Bismark for being too cautious and anti-war.