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Although Jesus was likely to have spoken Aramaic or Hebrew, the Gospels were preserved in Greek using the word πατήρ/πάτερ, as was noted in the comments; this became the Latin pater. In England up to the Reformation, liturgically the Lord's Prayer was always in Latin.
However, Wikisource has Old English (10th–11th century) and Middle English (14th century) versions†:
Fæder ūre, þū þe eart on heofonum;
Sīe þīn nama gehālgod,
Oure fadir that art in heuenes,
halewid be thi name;
The word was cognate with the modern English Father. Whether Fæder or fadir were as formal as "Father" is today is not easily discovered, but it's likely that they were not; children routinely addressed their parents as "Mother" and "Father" until comparatively recently, and OED does not have Dad/Daddy recorded until the 16th century.
† The later version is from Tyndale's Bible. The earlier source is not identified.