The Franco-Prussian war was one of the first wars in history which proved that logistics had become one of the most important parts of modern warfare. While in the centuries before many battles were decided directly on the battlefield, the Franco-Prussian war was decided before the first battles.

Germany/Prussia had a vastly superior mobilization system in place which allowed to raise operational armies and bring them to the front in stunningly low time ( for this time period ). Comparable to WW2 the first weeks/months of actions came to a great surprise for neutral observers who expected warfare of the past. Constant preparation and advancement in Prussian General Staff changed the face of war.

It is important to understand that Prussia was badly beaten by Napoleon and later was putting more effort into improving its military. The Prussian army in the late 19th century was likely the most advanced army in the world in terms of doctrine this was seriously exacerbated by their modern mobilization system which resulted in an unprecedented swift victory on this scale.

When the decisions for war were made on both sides, the mobilization began. German soldiers were raised in the so-called "Wehrkreise" which meant soldiers would be pooled in a rather small area to form units directly in their Wehrkreis which then could immediately be moved. The infantry of a German regiment was mostly from the same area or even cities. This often allowed soldiers to reach their designated assembly area within days and start organizing while French soldiers were moving all over the place in France trying to reach their designated units. The Prussian system was very advanced for its time and most of the units were accounted for and their whereabouts known at all time.

Comparable to World War 1 the German plans for the attacks were laid out long before a war was on the horizont. Like in World War 1 Germany was planning to always lead the attack and dictate the battles. The planning was meticulous and the mobilization and movement scheme was already drafted. The railway system for the first time in history was of essential importance to the movement of armies. Comparable to the Autobahns in WW2 the railway system was influenced by the military and their expectation to use this transport system.

Three days before the French declaration of war was send German forces were already mobilizing and preparing to march. Within few weeks German forces launched their first attacks into French territory.

Despite being willing to wage war against Prussia/German states and declaring war the French army now was outnumbered 2:1 on its borders against an enemy who had a smaller regular army some weeks earlier and with longer traveling distances. German armies all of the border were now overrunning small surprised French forces.

The series of surprising victories led to a near collapse of the regular French forces which were the best-trained units available to France. Now reserve and newly raised units were to fight against seasoned Prussian units. The Prussian army was superior in general but now fighting against even weaker units led to some loopsided battles.

Some general comments about casualties in wars:

Depending on the scale, the losing side will always suffer higher casualties. There are several reasons for this. First of all the losing side often gets disorganized towards the end which decreased their fighting power greatly. The losing side will have trouble to care for its wounded. The losing side will lose many soldiers as POWs.

The losing side will also be more willing to try hazardous attacks in order to regain the initiative.

Superiority in numbers in itself is a force multiplier which means the smaller forces should suffer more casualties. Beginning with the Franco-Prussian war the artillery became more and more important, culminating in World War 1 and 2 were artillery expenditure was one of the most important parts of all armies. Prussian forces had a superior Artillery doctrine which again resulted in higher number of French casualties.

Edit: There was no "German" per se during this war but I use the term to describe the Northern Bund and its southern allies.