Disclaimer: I've been away from France long enough to waive any responsibility in the up-to-date-ness of this information. Who knows, things might have changed. In doubt, follow these guidelines and observe the behaviour of your business partners.
** Looking forward to seeing your edits here **
Hand shaking: Each time you meet with someone, even if you already know the person. Usually you say hi by shaking the person's hand. If you attend a formal meeting and leave, shake everyone's hand again to say goodbye. Also shake hands when you haven't seen the person in a while. If you come into an office/meeting every day for let's say a week, observe what the others do and adopt the same attitude. A hand shake might not be necessary anymore.
Kiss on the cheek: Only for people who know each others. Basically you press your cheek against the person's and kiss the air. Warning: depending on the region in France you start with the right side, or the left side. That can lead to awkward moments if you make a mistake somewhere in the middle In doubt, start with the left cheek. This is the Parisian way. Also, observe the locals because sometimes there's one kiss, two kisses, four kisses as well.
You shouldn't attempt to do the kiss on the cheek until your female counterpart has made the initial move.
In a business situation, the kiss on the cheek is more for colleagues who know each other well.
** I'm adding a map of France with information on the kiss for a funny note to this page **
Hugs: The good hug is not very frequent in France. Friends greet each other by kissing on the cheek. When they say hi and goodbye (and even in a group of let's say 10 people!)
Salutation: Always use "Monsieur [Last Name]" for a man and "Madame [Last Name]" for a woman when you address the person for the first time, especially if you're meeting with customers or business partners. Observe if the person decides to speak to you using the first name and do the same. Note that most of the times, colleagues use the first name and use the formal "tu" instead of "vous". This is the case at SAP France for instance.
Can be pretty formal. Though one can notice that Fridays are more and more casual.
Dress formally and if needed and unsure, ask if the company observes the "casual Friday" attitude. Usually they don't.
Be open to disgressions. The French like to talk about art, culture, food, etc.
Discussions can be intense and passionate, this doesn't mean that the person is angry.
Avoid political topics.
Eye contact is important.
Don't chew gum, it is considered vulgar.
Money can be taboo. Don't brag about how much you make or how big your pool is.
Learn a couple of French words to show that you are interested in their language.
In a business lunch/dinner, wait for everyone to get their dish before starting eating
Be on time. If you're running late, call the person you are about to meet. Arriving more than 15 minutes late is rude. In the South of France though, punctuality can be a more flexible concept. Check for strikes that may disrupt public transportation the day of your meeting.
Action items appear throughout the meeting and are not always summarized in the end. Unlike North American which will commonly try to summarize.
The French, especially in the capital Paris, may start later around 9am or 9:30am. And they will finish around 6-7pm, sometimes later.
Long lunch breaks are common (1.5 hour to 2 hours). The French may drink alcohol during their lunch break.
When a French colleague says 'No' or 'Impossible' to your idea, this is the beginning of the conversation not the end. They simply want to be heard. In North America this is commonly interpreted as the end of the conversation.