It all depends on your experience level and total time. If you have ATP and you manage to get hired by a JAA carrier, you can validate" your FAA ATP. You must have FAA type rating for the airplane you are going to be flying in JAA carrier. Once you are done with the operators training you will be issued a validation of your FAA ATP (all based on FAA type rating and license, including FAA 1st class medical for the duration of validation).
Validation is good for 1 year during which you must take all 14 JAA ATPL written exams. If you have at least 1500 PIC you can do this as a self-study, no classroom required. Once all written exams are done, you will be issued the JAA ATPL after your next company proficiency check.
Not easy but can be done if you have the right experience. Of course right now might not be the easiest time to get hired in Europe, but good luck.
I have not done this myself, but I know somebody who is in the middle of the process. JAA written tests are quite difficult compared to the FAA ATP.(14000 question bank).
This is all I know about this, check with your local JAA authorities about validation.
This would be almost free + you get paid while working for one year.