Key to correctly answering this question is differentiating between choice (A) and choice (C).
Considered within the context of the sentence, choice (A) may sound a little better than choice (C) does, but in order to consistently answer SC questions correctly, we have to go beyond using the way the choices sound, especially as, in higher level questions, incorrect answers are often written to sound correct and correct answers are written to sound incorrect.
It may also be tempting to decide that (A) is better because it matches the preceding clause by using the passive voice. While that take is related to why (A) is better, it isn't completely valid, as active and passive can be correctly used in different clauses in a sentence and even within the same clause.
Consider the following perfectly correct example.
Jenna was hired on Tuesday, and she started working on Wednesday. - passive then active
So, what truly makes (A) better than (C)?
Meaning.
Let's look at the sentence created via the use of (C).
In many upper class Egyptian homes, French was spoken within the family, just as the Russian aristocracy had once done.
Let's think about what that version conveys. We can cross off the opening modifier to make the sentence simpler and, in doing so, make the issue clearer.
In many upper class Egyptian homes, French was spoken within the family, just as the Russian aristocracy had once done.
Notice that the sentence says, essentially, "French
was spoken ... just as the Russian aristocracy
had ... done."
It becomes clear that this version illogically compares what French "was" with what the Russian aristocracy "had ... done."
Moreover, if we ask ourselves what the Russian aristocracy "had ... done," the only verb that "had ... done" could refer to is "was spoken."
So, let's substitute "was spoken" for "had ... done." We get "French
was spoken ... just as the Russian aristocracy
was spoken."
We can see that this version seems to convey the nonsensical meaning that French was spoken within the family just as the Russian aristocracy was once spoken within the family.
So, the (C) version is an illogical mess.
Now, let's look at the sentence created via the use of (A).
In many upper class Egyptian homes, French was spoken within the family, just as it had once been among the Russian aristocracy.
This version conveys the logical meaning that French was spoken within the family, just as French had once been spoken among the Russian aristocracy.
That difference in meaning is what makes (A) better than (C).