The airport is situated on French soil, close to the Swiss border. There is an exit to France and an exit to Switzerland; from the Swiss exit, you can only take a road that leads to Switzerland. The buses to Switzerland (to Basel) leave from the Swiss side; the buses to France (including the Saint-Louis railway station from which you can take a train to Basel) and to Germany leave from the French side. There are car parks and care rentals on both sides.
Most visas for Schengen countries allow travel all over the Schengen area. If your visa requires that you declare which country you will enter first, pick either France or Switzerland depending on which exit you intend to take. In fact, this logically shouldn't matter, since there is a border point that you can cross right in the airport, so you could exit on one side and immediately cross the border; of course logic doesn't always matter when it comes to border crossings.
If your visa requires declaring which countries you will visit, pick France if you're going to France and Switzerland if you're going to Switzerland. If you're going to Germany, you'll probably want to enter on the Swiss side and take the bus to Basel, but there is also a bus to Freiburg that leaves on the French side. There is no longer a way to reach Germany without crossing either France or Switzerland. On this questionthis question you will find more information on getting to Germany.
