Beowulf is actually Old English, Norse. The language used is Anglo-Saxon (a/k/a Old English) and it predates the Middle Ages (Medieval time) by several hundred years. It was committed to writing in the 800's, but the story itself came from the oral tradition and is probably hundreds of years earlier. It's very pre-Christian and has all the typical Germanic elements. When it was committed to writing, the writing was done by Christian monks who attempted to Christianize this epic saga; those parts kind of stand out like a sore thumb in the original.
The basic story line is as you describe - one can just imagine some bard picking up his lyre late at night in a mead-hall when the fire starts to become embers and begins to tell the saga of Beowulf. Must have been awesome. It's essentially the ultimate "scary campfire story".
Many of the individuals mentioned were some of the legendary first rulers of the Germanic people which further evidences the saga's age.