Is it enough to show the PDF file on my smartphone to validate or I need to get a physical ticket?
I'm not familiar with any RER train tickets that can be bought online, besides through the 3 official Paris train transport mobile phone ticket apps provided by the city / regional transit authorities. And those do provide email receipts, but those are simply for your records, not for use as tickets. The ticket would be stored on the phone itself and validated using the phone's NFC chip.
I'm also not familiar with any method of ticket redemption via printed email confirmation at RER ticket windows in Paris or CDG Airport train stations.
If you could post another question with more information on the website from where you purchased the tickets, perhaps I could investigate and give some advice. (Sorry, there's no way to reply to my message here in the same thread.)