Just take it easy. It´s pretty normal to be a little nervous when you´re making your first trip abroad.
But you´ll be fine. I´ve made a few transatlantic trips and it was fine. No big difference to regional flights, really.
With the 340 you´ve got a very safe plane, indeed. And, by all accounts, a pretty comfortable one as well.
I like to take a good book with me. Listening to music or watching movies will also help for a nice trip.
Bon voyage and welcome to Europe!