The modern English language has many French influences. Why doesn't the language of Beowulf, Old English, reflect these influences?
The Anglo-Saxons hated the tribes from the modern-day France area and did not mingle with them.
This poem was written in a more formal version of Old English. The vernacular version of Old English does have French influences.
The Norman conquest occurred after the transcription of Beowulf.
Invading French tribes tended to settle near the Celtic tribes in the west of England, near modern-day Wales. They did not mingle with the Angles, Saxons and Jutes and so did not yet influence the language.
French influence in early Old English faded away as the language developed over time.