To clarify the framerates, film is, and always has been, 24fps.
The PAL system is a 50Hz signal, 50 fields per second, equivalent to 25 frames per second.
To convert from 24fps to 25fps is a simple case of speeding the film up. Most of the time this is unnoticeable. (Alternatively you can keep it 24fps and mess around with non-standard pulldown and blended fields - but this looks a mess, and thankfully is very rare).
NTSC was originally 60Hz, but this was reduced to 59.94Hz when colour was added. That's 29.97 full frames per second.
A speed up from 24fps up to 29.97fps would be unacceptable, so instead a system of repeated fields was devised. You cannot simply repeat every fourth frame because the jerkiness would be a problem. What happens is every 2 film frames are split over 5 fields (3:2 pulldown). This keeps the jerkiness to a minimum (altough PAL users, who are used to smooth motion, can sometimes see the effects of pulldown on motion and camera pans.) You end up with 4 film frames spread over 5 video frames, equivalent to 4/5 * 29.97 = 23.976fps. (No-one ever complains about the slowdown from 24 fps to 23.976fps!)