The answer to this question, is probably no. There doesn't appear to be any significant historical evidence pointing to Charlemagne traveling beyond Italy. However, there is perhaps one exception......The Aachen Palace-Cathedral.
It is well known within historical circles that Charlemagne was very impressed with the Saint Sophia Cathedral in Constantinople. He was so impressed with the Saint Sophia's architecture that he commissioned his Palace-Cathedral in Aachen to be designed in the Byzantine style-(namely the Cathedral's interior).
Now it is likely the case that Charlemagne's Architect(s) may have been the ones who visited the Saint Sophia Cathedral in Constantinople and wrote blueprints for the architectural style of the Aachen Palace-Cathedral. But, then again, perhaps Charlemagne himself visited Constantinople on a rare State or Diplomatic visit and viewed the Saint Sophia Cathedral with his own eyes.
Again, it seems unlikely that Charlemagne traveled beyond Italy; however there may be some available historical evidence which would contradict such a traditionally held position.