Cleopatra was a Ptolemy and the Ptolemies were Greek. They were also notorious for inbreeding so it's more likely than not that her mother was one of them.
Yeah, Egypt was given to the Greek general Ptolemy by Alexander the Great when he divided his empire up between his generals upon his death. The ruling family in-bred in order to not mix with the local population, and never even learned Egyptian.
Cleopatra was married to her little brother (although they probably never slept together), and was also the first in her family to speak Egyptian, and identify as an Egyptian rather than separate ruling-class Greek. It's part of what won her the civil war against her brother-husband. Although it must be said that a lot of this comes from the Romans and you can never trust the Romans with another country's history. They are almost as bad as the Victorians and that is saying something.
I don't think that comment about DNA tests showing her mother was African can be correct, as her tomb has never been found (a possible find from earlier this century has never been substantiated). However it is of course possible that Afrian blood entered the family line at some point due to lack of records, particularly (of course) of women.
It bugs me no end that Cleopatra is often called a Pharaoh. She was a Queen who came centuries later than the Pharaoes.
The Pharaohs, who came loooong before the Ptolemys, though, would have been Black, or at least Arab-looking. And of course most of the people living in Egypt would have during both these periods looked pretty much like Egyptians look now, with some migrants from other places scattered about.
I think in terms of accurate filmmaking (and really, where's the fun in that?) I don't give a jot if they make Cleopatra Black or Arab, as it's in the realm of possibility. But the wholesale whitewashing of Egyptians and 'Phararohs' is a bit
You can't make every non-white person white (Avatar the last airbender, Ghost in the Shell etcetcetc), and then bitch when one 'white' character is made non-white.