Actually, the Franco-Prussian War is only called by that name outside of Germany. We Germans tend to call it the "Franco-German War", which is a bit more correct, since other German states such as Bavaria fought in it as well.
One of the main reasons Germany was able to win this war was the relative obsolescence of French military hardware. For example, most of the French cannon were smooth-bore muzzle loaders, while the Germans had breech-loading, rifled guns. The French had a funky Gatling-type machine gun, the Mitrailleuse, but that didn't quite cut it for them.