I don't think Jonathan Rhys Meyers has found the right part yet since the Tudors competed its run. He was excellent in that series. He's performed well in diverse projects like Ride the Devil, Matchpoint, and Bend it like Beckham. I enjoyed the Children of Huang Shi since he and Radha Mitchell had chemistry, though it wasn't a popular film.
His American accent was unnecessary and it sounded forced. I have no idea why it was necessary to use that. So many English actors also speak French. It would have made more sense to use that kind of accent instead if at all.
Changing such a famous story is always going to be a problem. Some stories are timeless and there's no need to reinvent them. Can you imagine altering The Godfather? People would have a cow.