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Girona Airport, does not currently have a Train Connection. Girona Airport is currently undergoing some major changes, and if you haven't been their in a while, you may not even recognize the Airport.
You can however, get a Bus from Girona Airport to Girona Centre, and carry on to such places as Barcelona, Lloret de Mar and Figueres.
For more information on Train Timetables, visit the RENFE website.
You can find more information on the Girona Airport Train to Bus Connection, inside the Airport.