however I see from the PARAFE website
Given every answer I am giving is sourced from http://www.parafe.gouv.fr care to tell us which website you read? I am asking because for example ESTA is notorious for scam websites and if there's a PARAFE scam site we need to know about that to warn people.
I need to register for the service before use.
You are correct: "citizens of the European Union, the European Economic Area (EEE) or Switzerland" are entitled to use the service but "if you do not have
a French biometric passport, you must first register for PARAFE." leaflet
During a layover, can I go to the appropriate terminal and enroll?
Yes, in fact the only way to do this is airside. At Paris Charles de Gaulle Airport, Terminal 1: Departures level – by gate 24 and Terminal 2 E: Departures level – by gate 10 (the leaflet promised a Terminal 2 A/C, departure level opening in 2012 not quite sure what happened to that). At Paris Orly Airport: Orly Sud: Departures level – Boarding Area A. FAQ
How long will it be valid for?
"Registration is valid for 5 years and valid at all airports which are equipped, or to be equipped with the PARAFE facility." http://www.parafe.gouv.fr/wp-content/uploads/2012/06/Fiche-Modalites-PARAFES-GB.pdf and http://www.parafe.gouv.fr/en/category/vous-ne-possedez-pas-de-passeport-biometrique/
Will obtaining a new passport require me to re-register?
"If any passengers have changed their passport, what should they do ? They should return to the registration lounge with their new passport, and the information will be registered by a police officer." FAQ, page 4, question 18