The Franco-Prussian War is in the transitional period between linear warfare and the kind of firepower-based, railway-enabled warfare we would recognise from the start of the First World War. Both sides used single-shot bolt-action rifles, but the French went to war in uniforms that were effectively updates of those their grandfathers had worn fighting under Napoleon. The Prussians' uniforms were a bit less fancy but no less conspicuous.

Prevailing opinion in Europe at the start of the war was that France would win: it had a larger population, and ten years earlier it had given the Austrians a good battering in the Second Italian War of Independence. Its soldiers had more modern weapons: the Chassepot, the standard issue bolt-action, single-shot rifle, was much more modern than the Prussian Dreyse needle gun, more comfortable to fire, and much more accurate at range. They also had a primitive machine gun, the Mitrailleuse, a multi-barrelled miniature cannon that could fire 25 balls at a rate of 100 rounds per minute.

Unfortunately for the French, their doctrine and organisation was incredibly poor. The Mitrailleuse was seen as an artillery weapon and was deployed accordingly, and so lacked utility as an infantry support weapon. It was also seen as a "secret weapon": Marshal MacMahon, the French commander at the Battle of Sedan, claimed he'd never even heard of it until one was wheeled past his headquarters. French conscripts were generally undisciplined and often slacked off: French soldiers at Sedan actually broke international law by slipping away from their camps to visit bars and cafes over the border in Belgium, which was neutral. There was a critical lack of trained staff officers: officers saw staff duty as boring and unglamorous and stuck to regimental duties whenever they could. Consequently the French system of mobilisation was shambolic and resulted in many thousands of stragglers. It's illuminating that that although France had a larger population than Prussia and its allies, at the outbreak of war Prussia mobilised 50,000 more soldiers than the French. Recognising the deficiencies of their infantry, French tactics were almost wholly defensive, and aimed at establishing bases of fire that the enemy would have to attack so he could be destroyed by the power of the Chassepot and Mitrailleuse.

The Prussians in contrast were spectacularly well-organised and had spent the past four years digesting the lessons of the war with Austria in 1866. The deficiencies of the Dreyse were more than made up by their artillery, steel-barrelled, rifled breech-loading Krupp pieces that were probably the most modern in Europe. The French were still using cast bronze muzzle-loaders. Its infantry were trained to fight aggressively, fighting in loose order, with every man making maximum use of the rate of fire of his weapon and closing with the enemy using tactics reminiscent of modern fire and movement. The Prussian General Staff was the only one of its kind in Europe, devoted to analysing the lessons of past conflicts and developing the aforementioned mobilisation plan that allowed Prussia to concentrate superior numbers on the French frontier on the outbreak of war.

The Prussian cavalry had been substantially reformed after the Austro-Prussian War: the Battle of Königgrätz had seen the cavalry, the supposed "arm of decision", ingloriously stuck well behind the battlefield as infantry, ambulances and supplies struggled to get forward, thus denying the opportunity of pursuit when the Austrians finally broke. By 1870 the Prussian cavalry had been lightened, with much less elaborate uniforms and an emphasis on reconnaissance, skirmishing and providing flank security to the infantry, rather than the charge. Prussian tactics were offensive: recognising the growing superiority of firepower, they made full use of what we would now recognised as decentralised Mission Command to control their forces, marching as corps with the aim of collapsing around the enemy position rather than attacking it directly.

When it came to the fight, the Prussians on the whole got the better of the French. This is not to say that they did not make mistakes: General Steinmetz demonstrated a blithe disregard of General Staff instructions and Prussian doctrine, while the August battles at Spicheren, Wissembourg and Froeschwiller were stumbled into rather than planned. The Prussian infantry would take horrendous casualties in frontal attacks in these battles before their commanders managed to work out the French dispositions and get messages to neighbouring corps to attack their flanks. However, where there were Prussian mistakes, the French system meant that there was no initiative to take advantage of them. Marshal Bazaine demonstrated almost no offensive spirit: at the Battle of Mars-la-Tour, two Prussian corps attacked the entire French Army of the Rhine, mistakenly believing it to be just their rearguard. They were outnumbered four-to-one, but the French never counterattacked.

Sources:

Christopher Clark, Iron Kingdom: The Rise and Downfall of Prussia, 1600-1947

Geoffrey Wawro, The Franco-Prussian War: The German Conquest of France in 1870-1871