First of all, if i am not wrong you could have a TM problem with this name, second, i dont really see how the .eu could have any value, in USA he is barely known, if it would be .es then maybe (Im spanish, J. Bardem is spanish, and is better known in spanish-language environments, with the oscar stuff it could have a glance of value but only if developed imo).
You would need the confirmation from other users more experienced than me about the TM issue but i would take care with it :S
Best of luck.
Eth.