Hello ncusack,
To qualify as a candidate to the European Airlines you will require something called a JAA ATPL. This can be a full ATPL or a "frozen" ATPL.
You cannot apply to european airlines unless you have a JAA licence, so an FAA ATP simply won't do in the case of european airlines (however it is nice to have both countries licences - opens up the corporate market a bit more especially with more and more N reg bizjets in Europe now).
The route to one of those coverted licences normally takes the following route:
1) JAA PPL.
2) Hour Building to 150 Hours Total Time (inc 100 Hours P1).
3) Study for and pass ATPL Exams. This normally consists of 2 modules with exams at the end of each module. This step can be whilst carrying out step 2 (see above).
4) Once you have Steps 1, 2 and 3 you can train for the JAA CPL.
5) JAA IR (Multi Engine - NOT Single Engine) Course.
6) MCC / CRM Course
7) JAA FI(R) - Flight Instructor rating (restricted - ie no sending out students on their first solos etc) - not an essential rating but quite practical, especially in this day and age with **many** more applicants then there are airline jobs!!!
At the end of that lot you will have a JAA CPL/IR with MCC/CRM courses completed. As you will have passed your ATPL Ground Exams this will also mean you effectively have a JAA "frozen" ATPL. The ATPL will become a full one (ie, not frozen) once you have enough hours, 1500 total with something like 500 multi crew time (on aeroplanes requiring two pilots) among other requirements.
Airlines such as Ryanair, Easyjet, etc... require you to have a JAA ATPL that is either full ("un-frozen") or frozen. Ie, at a bare minimum you will require a JAA CPL/IR (multi) with the ATPL Examinations passed. You cannot be a captain of an airliner until you have a full JAA ATPL (and considerable experience in the right hand seat).
There is another route to the modular route above and that is integrated. The integrated route takes you from 0 hours all the way up to a JAA "frozen" ATPL with around 200 hours total time in a little over a year, but it is an expensive option (well both routes are extremely expensive!).
Good luck and Best wishes,
Charlie Zulu