The usage of Bonjour and Au revoir carries a more important cultural meaning than the use of Hello and Goodbye in the United States. I am going to focus on it's use in everyday settings such as shopping or going to the doctor. We already know to say hello and goodbye in social settings among friends.
Let's start with shopping, especially shopping in a smaller boutique or "magasin". When you enter the shop, you always try to catch the eye of the person working there and say "Bonjour Madame" (or Monsieur). Note - you shouldn't say just "Bonjour" that is considered a bit too informal. The clerk will always answer back with a "Bonjour Madame" of their own. Of course there are times when the person may be busy with another customer and you don't want to interrupt. But just give it a few minutes and the clerk will catch your eye to say hello.
I'm not sure how to explain how this is different from shopping in the U.S. We are, of course, very often politely greeted when entering a store, especially a smaller one. But it isn't a ritual the way it is in France. If you want to let a French person know you're a tourist right away, simply walk into a small shop and don't say anything. Only very large department stores will bypass this custom - but even then if you, for example, visit the shoe department of a large store, the person working that department will greet you and expect to be greeted in return. Or if you end up purchasing something the rule will apply with whoever helps you at the checkout counter.
The same rule applies when you leave the shop, even if you don't buy anything. You are free, and welcome to enter any shop to look around. Just remember to say Bonjour Madame when you arrive and "Merci - Au Revoir" when you leave. If you have talked with someone or purchased something then a Bonne Journee (Have a good day) is often thrown in along with your goodbyes.
This custom means you are constantly saying Bonjour Madame, Au Revoir, Merci, Bonne Journee. You stop at a fast food counter for a coffee and pastry to go: Bonjour Madame (order and pay), Merci, Au Revoir, Bonne journee. And repeat when you walk in the boulangerie to buy your bread for the day, when you go to a restaurant for lunch, when you stop at the pharmacy for some aspirin, every time you walk into a shop, and at checkout when buying groceries.
Again - I'm not sure why, but I really enjoy this part of living in France. I guess it's because I feel like I fit in just a little bit more. I also know that I'm being a much more "Polite American" by following this simple, and I guess expected rule.
But - there's more. You don't just say bonjour when going into a store. A couple of other examples. You're sitting at a small pizza restaurant enjoying your meal and someone walks in for carryout. Most likely they will say a quick Bonjour addressed to everyone in the restaurant.
Another example: You're in the waiting room at the doctors office with six or seven other people and someone else enters. Many times, but not always, they will greet then entire room. In this case when there is a mix of women and men the person entering will most likely say "Bonjour Messieurs Dames", addressing ladies and gentlemen in one phrase. Those already seated will reply (not too loudly) - Bonjour Monsieur.
With all of the "Bonjouring" going on you may be surprised that the French often do NOT say hello if your are walking down the street or taking a walk in the park. Of course we don't do this in the U.S. in larger towns on a busy street, but in the U.S. I almost always say hello or nod my head when I'm out for a walk and someone else walks by me in the other direction. (For my friends in the Midwest - rest assured that the "lift the index finger wave" while driving is NOT done in France, a habit I have trouble giving up).
I take a lot of walks and bike rides in France and I usually say Bonjour to most people I meet - just because it's habit. The other person will almost always politely return the greeting although it isn't expected. Oh - and even in this very informal setting of just going for a walk you should say "Bonjour Madame" rather than a simple "Bonjour" . Especially if the person is obviously older than you.
So this is an easy one. Before you come to France for vacation get in the habit of politely (and not loudly), extending a greeting and farewell in almost any situation. Know these few simple words and you will go a long way in giving Americans a good name while you're in France:
Bonjour (hello or literally good day)
Merci (thank you)
Au Revoir (goodbye)
Bonne Journee (have a good "rest" of your day - said when you leave).
Madame (Madam - married or older)
Mademoiselle (younger girl or woman, not married. When in doubt always use Madame)
Messieurs Dames (Ladies and gentlemen - uses to address a group of people with one phrase)
I hope you enjoyed this little lesson in simple French etiquette. Have you experienced this cultural difference in France or anywhere else?
I would love to hear you comments and your experiences. I will try my best to answer any questions.