No problems at all. You don't need anything on the aircrew licencing side of things. Remember that anyone flying or maintaining your aircraft will have to have FAA tickets. Other than that - away you go. The authorities may have to look at it on the customs side of things but not on the aviation side.
If you are going to be flying in Europe in general, read up on the local regs and airports before you go as they have some very specific ways of doing things (Nice airport comes to mind straight away). Nothing too huge but you have to know what you are doing. In France, if you intend on landing at HLS's other than at airports, you will need a Helisurface permit which will cover you as the pilot but does not negate the need to get approvals to use the actual HLS.
Spain, France, Italy, Germany & Greece do not need specific approval to operate in their airspace. Greece (for example) requires a written flight plan faxed to them for each flight and you will need ground handler assistance at the airport you are going to.
There are alot of foreign aircraft flying around France (where do you think the Poms fly to when they want to get away?)
There would be alot of people on this forum who could add to this but it is not as hard as it seems.
Have fun
