Completely agree that in France a few words of French can go a long way and that it pays to be more formal when addressing people than we usually are in English. If you can say "Bonjour", "Merci", "Au revoir" and "Parlez-vous anglais?", that will go a long way towards oiling the wheels of social intercourse in shops and restaurants and so on. This is not entirely illogical: how would it seem to us if were shopkeepers in, say New York or London and a person walked in and just launched into French without asking if we could understand it? It would seem odd, at best.
Also, the French use "monsieur" and "madame" far, far more than we use "sir" and "madam" in English. So, it is perfectly usual to say to the shop assistant "Bonjour, monsieur" or "Bonjour, madame", similarly "Merci, monsieur", "Au revoir, madame", and so on. Indeed, a simple "Bonjour" can sound a bit brusque to the French ear.
By all means try more French than this, but you might find that once you've tried the person you're speaking to will happily try out his or her English, particularly if it's a younger person.
In Italy I've always found the locals great when it comes to the language. I try out my Italian (which is poor and gleaned from my knowledge of French), and they just laugh along with me (never at me): it often becomes very entertaining. Give it a whirl if you're there. The Italians have a most beautiful language, which they're rightly proud of, but they're not jealous of it when people speak it badly. Perhaps this is because most people also have a dialect that they speak in addition to the national tongue — I don't know.
Spanish I find much harder to pick up, but in the main tourist places you will find English speakers. Remember though that the native language in Barcelona is Catalan, a completely different language from Castilian Spanish (as different as, say, French is from Spanish). Even so, almost everyone will be able to speak Castilian, and I find that the locals will often address a tourist first in Castilian, presumably because they think that the visitor is more likely to know Spanish than Catalan. (Ironically, I find Catalan easier to understand than Spanish, although I can't say a word in it.)
In the smaller northern countries of western European that speak Germanic languages (the Netherlands, the Flemish part of Belgium, Denmark, Norway, Sweden) the standard of spoken English is often high — although it's not true that everyone will speak English. It's polite to assume that they might not on first encounter. However, most people involved in any way with the tourist trade in these countries are very likely to have at least an adequate command of the English language.
In Germany the general standard of spoken English is not quite as high, and in particular there are a lot of older people who really don't know it all. Even so, they do pretty well. A few words of German will not go amiss.
For younger people everywhere, the ubiquity of English-language pop songs means that it is difficult to exist without at least some knowledge of English. And in travelling terms, English is the most common lingua franca in most places: if a Hungarian is talking to a Swede or a Chinese person is talking to a Spaniard, the language that they are most likely to have in common is English.