Noun, derived from douche bag.
A Eurodouche is a European douche bag, one who believes himself or herself superior to others (mainly Americans) because he or she is European. One who exhibits an inflated sense of self because of European birth, culture, or current residence.
In America, the Eurodouche can typically be found in airports, about to return to Europe. He or she will be speaking a language other than English, mocking American food, people, or customs, and believing (naively) that no one else around him can understand. He or she will also be found in large American cities and universities.
The Eurodouche is often unaware that (some) Americans may have superior culture and knowledge, in extreme cases knowing more about the Eurodouche's country of origin or speaking the Eurodouche's mother tongue better than he or she.
Bobby: "Hey, look at that pretentious French guy over there, totally mocking the Americans around him. If he hates our country so much, why does he come to vacation and study here? Look at how he is dressed, jeans way too tight, ripped as if it were still the 80's, and with a T-shirt with silly English slang on it spelled incorrectly--so not cool."
Tommy: "Yeah, that guy is a total Eurodouche. Let's go speak to him in French. He doesn't realize that everyone in our group is fluent in French."