Here's some information on the relationship between Ancient Egyptian and Coptic:
The Spoken Language System: Some scholars hold that the ancient Egyptians had another language in addition to the written form. Father Shenouda Maher summarized the opinion of Chain concerning the popular national language of ancient Egypt, . . . in which he emphasizes that the Egyptian and Coptic languages have been together simultaneously since olden times. Chain has presented a copious and detailed study and has indicated that the Egyptian language is not a spoken language is so far as it is basically derived from Coptic, assuming that Coptic is the origin, and that the Egyptian language was used by the priests and the scribes in their written work only.
This means that the Egyptian language is the language of the Egyptian who spoke in Coptic and who used this language for scriptural purposes only. This Egyptian language was only known to scribes and totally unknown to the public.19
The two systems could be explained by assuming all Egyptian since very ancient times spoke one language, but this language took a different form when used in writing. The oral language was colloquial and used by the common people. Although the spoken language developed over time, it was not written during the rule of the pharaohs. As noted earlier, it was finally written in the third century A. D., utilizing the 31 letters from Greek and Demotic. Utilizing all of these letters allowed for the correct pronunciation of the written language, primarily because the ancient Egyptian did not include vowels.20
In any case, the Coptic language “is, at base, a dialect of Ancient Egyptian; many of the nouns and verbs found in the Hieroglyphic texts remain unchanged in Coptic, and a large number of others can, by making proper allowance for phonetic decay and dialectic differences, be identified without difficulty.”21