If hiring a car make sure you return it to the right side of the airport or you will face a big fee. I rented from Switzerland as it was cheaper but there was a sneaky cross-border fee of CHF 30 payable at the desk and as I was driving into Germany I had the hassle of crossing the border which added time both out and return. I assume if I rented from the French side that fuss would have been avoided.if you do the reverse remember you have to buy a vignette to travel in Switzerland, a rental car from the swiss side will have that included.

There was no immigration queue when we landed, my passport was stamped in as Mulhouse France and Basel Switzerland on the return home