All your JAA PPL training is allowed towards any FAA license or rating.
Relative to a JAA PPL, the FAA PPL had extra night flight requirements.
You also need to fly 3 hours within the 60 days preceeding the checkride, with an FAA CFI instructor who will sign you off as ready for the checkride.
You then have the checkride.
Before all that, you need to pass the one theory exam, and get yourself an FAA medical, which for purely private flying can be the Class 3.
The exam and the medical can be done in Europe but the flying is strongly recommended to be done in the USA. Some notes are
here.