You could actually have paid FedEx to have a courier travel with your package on the next United or OAL flight to Europe, where another FedEx guy would collect the package and have a van ready to deliver to the recipient. Alternatively, they can also offer to send it on their own plane, with personal delivery to the plane and similar handling after arrival, cutting several hours of the usual FedEx International First commitment of 2 days.

Note USPS Global Express is outsourced to FedEx (well at least to Europe). The only difference is that USPS brings it to the FedEx station instead of a courier coming to your place pick it up, and you don't need a FedEx account to use it.

While published FedEx rates are increasingly expensive, good INTL corporate rates can still be had if you're a good customer with a good account manager.

Otherwise, DHL Express offers similar transit times and tends to undercut the others in pricing.