Ancient Greek and Latin weren't dead yet during the Patristic period. Actually, neither ever did die, they just changed into the Romance languages and Modern Greek.
Yet they were not even CLOSE to being the language of the masses. Printing of the Bible in the vernacular was forbidden by the Church, specifically for the purpose of keeping it out of the reach of the common man. Most persons not within the priesthood were illiterate in those languages, including most royalty.