FedEx for sure does not allow any European operator to fly jet aircraft
One of the Turkish haulers (MNG or ACT), who by most standards qualififes as an European operator, are doing a run to TLV. Can't remember if it's for UPS or FedEx, but I'm leaning towards the latter.
Besides, UPS are going to run into ownership issues with TNT Airways. The rules say, by and large, max 49% of shares and no direct control for a non-EU company. This means the airline will have to be spun off, and it can either be terminated, handed over to someone else and forgotten, or handed over to someone else along with a long-term contract to operate x number of aircraft.
But TNT and UPS are both trucking companies with airlines added on as a bit of an afterthought. The real expansion is therefore likely to happen on the ground, and even with consolidation and all that's going to mean lots of jobs for European hauliers and at sorting/distribution centres. Which is all good, except if you're working in LGG and/or at TNT Airways or any of it's airport stations - consolidation on the aviation side is likely to outstrip growth and therefore jobs will be lost, on the ground and in the air in the short to medium term.