Charlemagne was King of the Franks (and Lombards), so naturally what language was his mother tongue? A form of Old German, or old French?
What language did the Frankish people speak?
Franks were a mixture of Germanic peoples, and Gauls, as well as Lombards and Romans. Which of these was most prevalent in the culture and being of the Frankish?
This previous thread has a lot of good points http://www.reddit.com/r/AskHistorians/comments/1emh7q/
The summary of it is that Charlemagne's native tongue was Old High German, though his biographer Einhard records that he "learnt Latin so well that he spoke it as fluently as his own tongue; but he understand Greek better than he could speak it."
Source: Lewis Thorpe's Penguin Classics edition of the Two Lives of Charlemagne by Einhard and Notker the Stammerer.
As for your question about the language and culture of the Franks themselves, I believe the linked thread has a good discussion about that same topic.