Fedex planes fly inter european routes but not unlimited. They use Air contractors (1 A300 and several ATRs), Westair (ATR-ATP) and Swiftair (ATR and EMB120).
UPS uses mainly STAR air (B767) , MNG cargo (A300), Bluebird cargo (B737) and Farnair (ATRs and F27) to fly within Europe.
DHL uses EAT (A300 and 757),DHL UK (757) in Europe.
Greetz
D