The peace terms that Bismarck negotiated with French representatives was actually quite severe and one that could hardly be characterized as asking for relatively little. Much of the conventional wisdom of the time held that indemnity would cripple France for the immediate future. Added to the bill of 5 billion Francs, the Germans not only received Alsace-Lorraine, an area that had significant fortresses, they were able to maintain an army of occupation within northeast France until Paris paid the indemnity. This was not a gentle peace.

The stringent nature of the French peace is apparent when contrasted to the terms Bismarck managed to hash out for the Austro-Prussian War. Both the Prussian military and King Wilhelm I had wanted to extract a large indemnity from Austria as well as annex Bohemia and a few other German-speaking regions of the Habsburg patrimony. Bismarck resisted both quarters and at a meeting with the King at Nikolsburg in July 1866, Bismarck actually threatened resignation and then suicide if Wilhelm I went through with demanding a more severe peace. Prussia received very little territory at the expense of the Habsburgs and a small sum from Vienna, which amounted to about 1/60th of the total sum demanded from France five years later. Of course, Bismarck's respect for defeated enemies only went as far to include great powers. Prussian not only annexed the free city of Frankfurt am Main, but also demanded from its burghers an enormous indemnity of 25-million guilders. So by this measure, Bismarck in 1871 not only breaking from his last precedent of a moderate peace, he was also treating France like a minor power.

That Bismarck was able to wrest both an indemnity and territory from France in itself was something remarkable. After Sedan, French representatives of the emerging republic were adamant that while a small indemnity might be possible, territorial concessions were a nonstarter. Jules Favre responded to one Prussian demand that the new government would "cede neither a clod of our earth nor a stone of our fortresses." In addition to denying the German's right to the soil of France, negotiations with the French also revealed that the French envisioned a far smaller indemnity than the one Bismarck eventually received.

French intransigence over the peace negotiations underlay the desperation of Prussia's post-Sedan moves. Although Sedan had destroyed much of France's professional armies and captured the Emperor, the successor regime was mobilizing on a scale that few within the German command relished. Simply put, the war continued to go on despite Germany having effectively won it. This was expensive and threatened the narrow consensus among the German states as well as opened up the possibility of foreign intervention. Bismarck did not particularly desire the latter and his instincts were to end the war quickly and at maximum benefit to the new German state. This desire to bring the French to heel underlay the bombardment of Paris, which worked after a fashion. Thiers agreed to both the indemnity and annexations, albeit with Bismarck reducing the indemnity by 1 billion Francs.

The indemnity itself was not a small number. France's outlays for the war itself amounted to approximately 10 billion Francs and 5 billion Francs amounted to about a quarter of prewar income. The expectation in Bismarck's circle as well as within the military leadership of the Prussian army was that this sum would take France the better part of three decades to pay off. The indemnity itself was much larger than most contemporaries expected; the Austrian ambassador to Prussia reported back to Vienna that he anticipated only 2 billion Francs to be demanded and Bismarck's personal banker Gerson von Bleichröder advised Bismarck that 4 billion Francs would be a ruinous payment.

There is some indication that Bismarck was hedging his bets with both the indemnity and the annexations as a means to buy time. In an August 1871 meeting with the French charge d'affaires in Berlin, Bismarck claimed that France would likely only part with 2 billion Francs before it sought out revenge. Although the August meeting was reflective of Bismarck's characteristic bluff and bullying approach to diplomacy, it does show he at least considered the possibility that France would not hold up its end of the peace. Moreover, by making such a harsh demands, Bismarck possibly calculated that it would buy Germany time to meet French revanchist thought. The sums for the indemnity were large enough to encourage dissent among the nascent Third Republic and Bismarck kept political lines open to the monarchists in French politics with the implicit promise that a more equitable arrangement could be possible with the right government in place in Paris. In the meantime, the initial indemnity allowed the newly unified German army to recoup its wartime budget and operate semi-independently from the Reichstag budget.

What shocked Berlin and something few accounted for after Sedan was that France was not only able to repay the indemnity but ahead of schedule in 1873. The Third Republic was able to finance two loans via J. P. Morgan and nationalist feeling was high enough to enable the government to bear the debt without significant political costs. Rather than dividing the French politics through a manageable Carthaginian peace and hamstringing French military recovery, the German demands on France actually did the opposite. In this, Bismarck greatly underestimated the growth of the modern state and the flexibility of international finance. Both of these factors, fueled by industrialization and modernization, allowed states to mobilize resources and money on unprecedented levels.

In this respect, Prussia's demands on France in 1871 were fighting the last war. While territorial adjustments and indemnities were the norm for peacemaking during the ancien regime, this system was growing increasingly inadequate as European states modernized. The Napoleonic period had already shown the inadequacies of this system as the French combination of indemnities and territory could not secure a lasting peace or even stave off hostilities from resuming after a few years. Napoleonic Prussia itself showed this lesson in that it was able to field a large army in 1813 despite earlier French demands for money and restrictions on its armed forces. In 1871, Bismarck may have moderated some of the more extreme demands of the military for a harsher peace, but he still pushed for, and received, concessions from the French that the Chancellor believed would cripple France for the foreseeable future. That France recovered far sooner than he expected became one of the major problems for German foreign policy in the coming decades. The concessions Bismarck wrung out of France were as harsh as politically possible at the time and they still did not suffice to keep France down.

Sources

Pflanze, Otto. Bismarck and the Development of Germany. 1: The Period of Unification, 1815-1871. Princeton: Princeton University press, 1990.

Stern, Fritz. Gold and Iron. New York: Vintage Books, 2013.

Wawro, Geoffrey. The Franco-Prussian War The German Conquest of France in 1870-1871. Cambridge: Cambridge Univ. Pr, 2010.

You are forgetting the most important thing Prussia got from the peace - Germany. Bismarck's primary goal in provoking the war with France was to use it as a political vehicle for German unification under the Prussian crown. The actual disputes with France were in many ways marginal - after all, the war technically was caused over a matter of diplomatic etiquette concerning the Spanish throne (see the Ems Telegram). It was far less important why the Germans fought the French than the fact that they were fighting, and as Germans.

Bismarck calculated, correctly, that the most effective method to unify Germany under Prussia was to harness German nationalism to that cause. Prussia would be the champion of the popular desire for a unified Germany, and the people and lesser states would flock to their banners. France provided a convenient and traditionally hated foe to provide the "them" for Bismarck's "us", and the resultant unity in the face of a common enemy was the nucleus around which the unified German Empire was created.

Having gotten the big prize, anything further would have been almost superfluous and needlessly antagonized world opinion. Bismarck had ably managed his diplomacy so that the powers of Europe, like Russia and Britain, did not interfere with his plans. Excessive demands against France would have endangered that, and even further antagonized the French. Per some sources, Bismarck was actually lukewarm or even opposed to the annexation of Alsace-Lorraine, seeing it (correctly) as a permanent point of contention between Germany and France.

Prussia didn't ask for little from the war, they asked for exactly what they wanted, German unification, and they got it. That was the strategic goal, and anything else would have been irrelevant or even detrimental to that goal.