Without knowing details about AirBnB's corporate structure, I assume they don't have any subsidiaries or offices or employees in France. That makes it hard (but not impossible) to compel them to follow French law, or local laws in France.
The easier option is to write a law that compels payment processors to disallow payments to or from a company that does XYZ, then declare AirBNB has done XYZ and cut off their payments. It's certainly possible to rent an apartment in Paris and have all the payments done outside of France, but it removes a lot of people from both sides of the market.
The other option is to work through courts internationally, but that's very slow and costly for things that aren't capital crimes. You basically have to get your government's diplomats to make the US State department care to do the interfacing.
