Its not possible to do it while you're studying for the exams because you have to have JAR-FCL CPL knowledge before starting the FI course (see Lasors section H page 3).
Also, you have to have 200 hours total time of which 150 hours are PIC (for PPL holders) before you can start the course, so in effect you will have to do all the hour building required for the CPL before you can start the FI course.
So its a bit of a non-starter I'm afraid.
PW