The Germans didn't really have better arms than the French, at least to begin with.
When the war started, the armies of the united German states fought against the French imperial army. The standard Prussian infantry shoulder arm at that time was the model 1842 Dreyse needle gun, the first widely available breech-loading rifle in history. In the wars of the 1860s, it had so badly outclassed the muzzle-loaders used by the Danish and Austrians that one could reasonably describe the needle gun of 1866 as a "war-winning weapon". But by 1870, the French had their own breech-loading rifle, the model 1866 chassepot, which outclassed the needle gun in effective range and accuracy. Since most of the German troops were needle-gun-armed Prussians, this gave French infantry a distinct advantage. On the other hand, the Bavarian army employed the natively manufactured model 1869 Werder rifle, since it was politically impossible for good southern Bavarians to use a Prussian weapon. The Werder was roughly as good as the chassepot.
Furthermore, the French had the use of a secret wonder-weapon, the mitrailleuse, an early form of machine gun. Secrecy and poor doctrine initially inhibited their use - they were initially placed alongside the French artillery because of their carriage, but they didn't have the range to fight from an artillery overwatch position - but within a few weeks, the French artillerists, who were usually able to count to ten without removing their socks, had figured them out and were siting them in deadly defensive positions.
The chassepot and mitrailleuse combined did devastating damage to the German forces. In 1864 and 1866, the Prussians were often able to stand on the defensive while the Danes and Austrians assumed the role of obliging enemy by charging into the teeth of deadly needle gun fire. In 1870, it was the Germans who usually assumed the tactical offensive, partially for operational reasons, but also because if they remained at range, the French would be able to pick them off while the limited range of their own weapons would prevent them from responding in kind. The battles of the first month of the war - August and early September - saw a horrifying amount of casualties among the German forces that can be attributed in part to superior French technology.
If the Germans did possess a technical advantage it was in artillery. The entire Prussian artillery service had been refitted with brand-new Krupp breech-loading steel rifled guns, which were generally superior to the muzzle-loading bronze guns the French used. But the advantage wasn't that significant, and the breech-loaders came with the defects of any other relatively new technology.
German artillery was clearly superior to the French throughout the war, and proved to be their one trump card in those early battles. But although the Germans did possess a technical advantage in artillery, the majority of the advantage was actually due to the artillery's organization and tactics. German gunner doctrine was vastly superior; instead of placing guns in an immobile reserve to support a main offensive that never came (like the French), the Germans pushed as many guns as they could into the fight as early as possible and kept them there. Organic corps artillery allowed each German corps to be a relatively independent organization and saved overly aggressive German commanders on more than one occasion, like at Mars-la-Tour, when Konstantin von Alvensleben tried to fight the entire French Army of the Rhine with just his III Corps and managed to hold out until reinforcements arrived through a combination of sheer ballsy boldness and a well-placed and -managed gun line.
If you're looking for a single explanation of German success and French lack thereof, it has to be found at the top. On the French side, Napoléon was officially in charge of the army, in emulation of his uncle. But unlike his uncle, Napoléon III was not a warlord and in fact possessed almost no military aptitude at all. This would not have been a problem if his subordinates were skilled and had a clear command structure, but they weren't and didn't. His two army commanders, Bazaine and MacMahon, were decent enough fighting generals who had essentially no capacity to administrate large formations of men and equipment. They were personally brave individuals who completely failed at every point to actually manage their armies in battle or on the march. In every single battle, Bazaine's Army of the Rhine in particular fought as individual corps, not as a unified whole, and despite the tenacity of French soldiers and the skill of individual corps and division commanders, they were defeated as individual corps. Operationally, the French had no plan; despite completing mobilization before the Prussians did, they failed to seize their advantage with an aggressive march into Germany, and instead occupied a few border towns and sat down to await developments. When the German offensive began, both commanders did little more than organize a shambling fighting retreat.
On the German side, higher command was inestimably superior. King Wilhelm was a veteran of the wars against Napoléon I and had been a professional soldier almost all his life. His chief of staff, Helmuth von Moltke, is widely regarded to be one of the finest general officers in history, the father of modern staff systems, and the architect of every one of Prussia's great victories. The Prussian army commanders were a mixed bag (one of them, Karl von Steinmetz, was an unmitigated, insubordinate disaster), but unlike Napoléon, Moltke managed to ride herd over them reasonably well. Other good military leaders included Edwin von Manteuffel, the Alvensleben brothers, Eduard von Fransecky, Albrecht Kronprinz von Sachsen, and the commander of the Prussian Guard's artillery, Kraft Karl August von Hohenlohe-Ingelfingen.
Time and again, French imperial forces won local defensive successes but were encircled due to poor coordination and command, or were simply withdrawn from battle for no good reason. After suffering early defeats in frontier fighting, Bazaine withdrew his Army of the Rhine toward the fortress of Metz, and MacMahon pulled his own army back to Châlons, ensuring that the numerically superior Germans could fall on one army, then the next, and defeat them in detail. Bazaine's soldiers bought him time at Vionville and Mars-la-Tour, but the French failed to coordinate against the numerically inferior Germans, allowing Moltke to rush more men to the sound of the guns and overwhelm the French as the day ended.
A few days later, at Gravelotte-St. Privat, the French infantry made a valiant stand against Prussian assaults on their fortifications, shattering charge after charge. The Prussian Guard was slaughtered when it tried a head-down rush over open ground at St. Privat in a disaster equal to Cold Harbor or Pickett's Charge, and on the southern flank in the Mance ravine the French broke most of two entire corps so badly that the King rode into the throngs of retreating soldiers and personally started swearing at them and whacking them with the flat of his sword to get them to go back to the fight. But by the end of the evening, however, the Saxons had worked their way around the French flank and forced the French to retreat. Bazaine spent the whole day rushing from crisis to crisis, not directing the reserves or issuing orders. The Imperial Guard stood idly by, instead of completing the Germans' rout...and at the end of the battle, it failed to stave off the retreat as well. Bazaine pulled back again and went to the fortress of Metz, which the Germans besieged with part of their army while they took the rest to defeat MacMahon.
Again, MacMahon's march was so ill-conceived and mismanaged that the Germans were able to fully encircle his army by maneuver before most of the fighting started. The night before the Battle of Sedan, one of the French corps commanders, Auguste Ducrot, took a look at the ring of German campfires stretching around the army, and commented, "We're in a chamber pot, and we're about to be s**t on." That's basically what happened. Sedan was a disaster at every level for the French, and Napoléon himself was captured.
If the war had been fought in the sixteenth century instead of the nineteenth, the capture of the Emperor would've meant the end of the war. Instead, the French government hijacked popular demonstrations in Paris to declare itself a republic and, once it became clear that the Germans would not end the war without some sort of territorial and financial indemnity, continue the fighting. The Republic, unlike the Empire, had a plan. It had men who were good organizers, and it had the numerical advantage that the Germans had possessed early in the war. The Germans had to fight at the end of long, vulnerable supply lines, subject to the depredations of terrorists and French military raiders, and most of the German armies were participating in the siege of Paris rather than fighting the republic's armies in the field. The fundamental problem, however, was that the French were trying to create a national army ex nihilo in months from men who, for the most part, had never fought before. MacMahon's and Bazaine's regulars had been forced to surrender; few veterans remained to leaven the ranks. Fundamentally, the French armies were simply too inexperienced to win. The Republic had generals both skilled and unskilled alike; all were defeated in their turn. They could not defeat the German armies in a time frame short enough to allow the relief of Paris before it capitulated to the besiegers.
Lots of that in international politics. Thanks for the explanation.
