However, I do agree with you that people then thought that world peace was achieved. The 1910 book "The Great Illusion" [2] ironically argued European war was unlikely to start due to the great economic costs of destroying trade between nations. It got the consequences right at least.
[1] https://en.wikipedia.org/wiki/Franco-Prussian_War [2] https://en.wikipedia.org/wiki/The_Great_Illusion
Eh... not really. Anger at the loss of Alsace-Lorraine peaked in the immediate aftermath of the Franco-Prussian War, when France couldn't do anything, but by the 1880s and 1890s, France had resigned itself to the loss. The massive divisions in French society under the Third Republic meant that it was in no position to do anything to reclaim it. A parallel might well be drawn to Finland's position today over Karelia: they'd certainly like it back, but they're not about to fight for it. It wasn't until World War I broke out that restoration of Alsace-Lorraine to French rule really became feasible, and hence it became a major war aim, but it wasn't a factor until after war had already broken out.
The arms race in question is the naval arms race between Britain and Germany, which itself subsided in 1912 because Germany couldn't afford to keep up.
There were Balkan wars and there were Indian wars, but the vast majority of Western population never served in combat.
And people started thinking that this is how it is going to be forever.