I am sorry if this is common knowledge but I am completely clueless about the aftermath of the German invasion. I thought that the Germans had invaded France. I never heard of a great revolution that returned France to the French. I would really like to understand better how France went back to France... or did Germany only keep territories on the border?
By the treaties of Versailles and Frankfurt in 1871, France ceded Alsace and Lorraine to the newly formed German Empire, itself a new polity recognized by the same treaties. France retained its sovereignty but lost its Emperor. It spent the next decade forming a republican government, the third republic, which would last until 1940.
for a broad overview, look at Geoffrey Wawro's 2003 book on Cambridge University Press.