On local news this AM the some customers have experienced problems renting cars on the Swiss side, but driving to France for the majority of their stay. No indication that customers who have done so are experiencing problems, but apparently some of the car agents are refusing to rent if they know this is the purpose. The problem is that taxes are collected in CH when product used mostly in the EU. Also, according to FR law, cars used for this purpose need to be imported and duties and fees charged.
There is no issue with cars rented on the French side of the airport and driven to either CH or FR. This can often be cheaper!
Although it is a little complicated going from international arrivals to the French sector (and vv) it can be done.
A list of agencies on both sides, and detailed instructions of how to get from one to the other, can be found
here.