Alsace is culturally, ethnically and linguistically distinct from the rest of France, and seems to have a strong sense of Germanic identity. Why couldn't it manage to become an independent country? Smaller areas that were nearby and neighboured France managed to become independent countries, e.g. Liechtenstein, Monaco and Luxembourg.
Huh. No-one answered you. I'll give it a shot. I was a historian once.
I think the thing is probably that however distinct it was, it was never so distinct that it wanted to be independent.
It's bigger than those other entities, and they had already been independent. Alsace is strategically and economically important, and it had been French certainly by the mid 1600s. I don't see how France could have easily let it be independent, whereas it didn;t much matter whether those other places were, and in fact Lux was within the Holland v Prussia conflict more than to do with France.
If you look at recent times, no way would the Alsatians wanted to be closer to Germany than France immediately post-war.
I think one of the things about the vision of the EU is actually to soften national identity when there are so many regions in Europe that are heavily influenced by more than one country.