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Yes, the train station is at the airport as it's been already said.
If you're tight on budget, here they offer rides for around 5 € one way.
I think it's a great alternative to the way overpriced swiss train system.
https://www.blablacar.es/search?fn=Ginebra%2C+Suiza&fc=46.204391%7C6.143158&fc...