I'd like to clear out that I don't know much about this war and my knowledge comes from Vikings/The Last Kingdom/Ck2.
During the Medieval Ages the global language was Latin, but as far as I know the Danes were very apart from the rest of Europe and had no knowledge of Latin. Am I wrong here? Did they communicate through Latin, did the Danes teach a prisoner to act as a translator, what was the deal?
To clear up some confusion:
Normans were of norse descent, but had lived in Normandy for generations, they spoke a dialect of French.
The people living in England, spoke Old English (Anglo-Saxon) or heavily norse-influenced Old English.
The Norse of the Vikings were to a certain degree mutually intelligible with each other.
The Norman French was something completely different.
"No one" except priests spoke Latin.