Frenchmen mostly shake hands: a firm, strong shake, looking into the eyes. If you are really happy to see the person, you may cover your handshake with your other hand.
Women shake hands in a professional situation, or if they don’t know each other at all, but move on to kissing very quickly, even at work among colleagues — with both genders. For example, you may arrive at a party and shake hands, then socialize, make friends, and get kissed when you leave.
The kiss is more of an air kiss, but the cheeks do touch, unlike the mocking American air kiss.
Parisians usually kiss twice, once on each cheek, and it will feel weird if you stop at one. In other parts of France, the French kiss up to 4 times!
Learn more about kissing and hugging in my French Politeness masterclass.
This is also a question of social class. The higher up in social class, the less kissing and more handshaking. In more relaxed social classes or with younger crowds, men often kiss each other. Always on the cheeks, usually twice. They may even hug a bit, but more of a “tap on the back” kind of motion, not a big American hug.
To learn how to avoid to accidentally say to someone you like that you are in love with them, study the uses for the verb aimer in French.
Another big faux pas to avoid: the verb “to kiss” embrasser ≠ baiser.
And memorize French love nicknames with this audio post.