Sure, the Euros could operate the JFK, but at what cost? We're basically talking about frigate navies here. The Brits are not about to take on a costly veteran ship that will rob money from their tight ship construction budgets.
Training would be handled by mostly consultants with a only a few active duty personnel. Many of our own sailors are trained by the very same consultants that would help out in this case.
The bottom line; it is workable and a GOOD idea.