The French side of the airport (which is called Bāle-Mulhouse) is Schengen territory. If you want to go to the city of Basel though, you have to enter the Swiss side (not Schengen).
I am not sure however if the airport has a EU "domestic" terminal where you can do EU arrival => EU / French side without going through immigration. I think that's possible in the new terminal but is it open alredy?
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truly yours.
airOli.