The French tend to be much more proper, aloof and private than we are in the US. Our efforts to be “friendly” can be interpreted by them as alarmingly inappropriate familiarity.
When it comes to friendship, the French believe in quality over quantity. Friendship implies a deep mutual affection and commitment toward an ongoing relationship. A person’s friends are a tight-knit group that see each other regularly and take part in each other’s lives. Because of this, friendship is not given freely or taken lightly.
Generally speaking, French people don’t have casual friends. Socially, you are seen as either a friend, an acquaintance, or a stranger. It is a breech of etiquette to presume to act like a friend or acquaintance, when you are simply a stranger.
It’s not to say that strangers are treated unkindly, in fact, the French believe strongly that every person should be shown respect and deserves to be treated politely. It’s also true that, just like anywhere, there are some very gregarious French people that adore meeting new people and make friends easily.
If you find that you are making fast-friends with a French person, then consider it an honor as it’s fairly unusual. Conversely, don’t be too quick to consider them rude if they don’t return your smile or make small-talk with you. It’s nothing personal.
If you want to make friends in France, it’s best to seek out those outgoing types just like you. I’d recommend attending a home cooked dinner hosted by someone interested in meeting travelers. It’s a great way to meet people and get a glimpse of life in France.