France has gained and lost territories for centuries, at times owning parts of modern day Spain and the low countries for instance. Alsace-Lorraine had been gained relatively recently. It was a fair distance from Paris, and the residents overwhelmingly spoke german dialects.
Why then was this territory such a sticking point in politics? I've read historians claim alliance between France and Germany was impossible because of Alsace Lorraine, and war inevitable.
Why was this region so much more important than Catalonia, Wallonia, or Quebec?
Industry! While the arguments that each country used to control the region were generally socially-political (shared cultural heritage / shared language / self determination), the true motive was much more economic. Alsace-Lorraine (and neighboring Saarland) which France also claimed after WWI were both rich in natural resources and highly industrialized. In her analysis of the postwar German economy, Caroline Fohlin (yes she's an economist not a historian) estimated that Germany lost:
15 percent of the arable land, 75 percent of iron ore deposits, 44 percent of pig iron production capacity, and 38 percent of steel production capacity.
(These numbers bundle all the German post-WWI territorial losses including colonies in the South Sea and Africa, which were obviously not industrial powerhouses)
Its much harder to say whether war was 'inevitable' without getting into alt-historical speculation, but its clear that the industrial base of Alsace-Lorraine was a major boon to the economy of whichever power could control it.
Source for Numbers:
In addition to the economic factors, it should be mentioned too that Alsace Lorraine was seized from France in a deliberately brutal and humiliating fashion; its annexation was part and parcel of the establishment of the German Empire, and thus also part and parcel of France's loss of dominance on the continent. Add to this the fact that the Germans carried out their occupation harshly, for instance during the Saverne Affair in 1913 when the German army led a violent crackdown against the locals for trivial reasons, and you can see why A-L's occupation was also a hole in the French psyche.
Just to add to the other answers, and I read this only recently in Rick Atkinsons The Guns at Last Light ...
At the same time as the Battle of the Bulge the Germans were also planning an operation against the Allied forces which had liberated Strabourg, the largest city in Alsace-Lorraine. Allied intelligence predicted the attach but when Eisenhower ordered Gen Devers to prepare a withdrawal to a shorter line, the French high command refused point blank to abandon Strasbourg.
Among the reasons they cited : Strasbourg was the town where the French National Anthem La Marseillaise was composed in 1792.