For all intent and purpose (ATC, border control, regulation) BSL is a French airport. With some exceptions / provisions for a "swiss" and a "german" sector. But it is France who runs the show.
Now that may be so ... however I would question the totality of this statement .... when there were French ATC strikes in the last few years, all flights from the Swiss sector operated correctly, and there are both French and Swiss border control officers (customs and immigration) on duty. Please correct me if I'm wrong ... but kindly please! ... as yes, the airport is built on French land with a gated road from Switzerland to the Swiss side, with border checkpoints on levels 2 and 3 (landside and airside) and that the 'airport' consists of two entities BSL (Swiss) and MLH (French) and a global reference EUR (Euroairport for both combined).
Wikipedia notes ....EuroAirport is one of the few airports in the world operated jointly by two countries, in this case France and Switzerland. It is governed by a 1949 international convention. The headquarters of the airport's operations are located in Blotzheim, France. The airport is located completely on French soil; it also has a Swiss customs border and is connected to the Swiss customs area by a 2.5-kilometre (1.6 mi)-long customs-free road to Basel, allowing air travellers access into Switzerland bypassing French customs clearance. The airport is operated via a state treaty established in 1946 wherein the two countries (Switzerland and France) are granted access to the airport without any customs or other border restrictions. The airport's board has eight members each from France and Switzerland and two advisers from Germany.
The airport building is split into two separate sections: Swiss and French. Though the entire airport is on French soil and under French jurisdiction, the Swiss authorities have the authority to apply Swiss laws regarding customs, medical services and police work in the Swiss section, including the customs road connecting Basel with the airport. French police are allowed to execute random checks in the Swiss section as well. With Switzerland joining the Schengen Treaty in March 2009, the air side was rearranged to include a Schengen and non-Schengen zone. As border control is staffed by both Swiss and French border officers, passengers departing to or arriving from non-Schengen countries may receive either a Swiss or French passport stamp, depending on which officer they happen to approach.
Due to its international status, EuroAirport has three IATA airport codes: BSL (Basel) is the Swiss code, MLH (Mulhouse) is the French code and EAP (EuroAirport) is the neutral code. The ICAO airport code is LFSB,
(My apologies that I cannot remove the embedded links or change the colour of them.)