How did the word 'familier' (French) become associated with the concept of Magical Familiars, historically?
Or do we not know?
The OED attests several use of the word familiar in Chaucer's works from the 1380's, in the usual sense of "pertaining to personal relations or family."
However the earliest use attested to in the OED in the sense of a familiar spirit is from 1584: R SCOTT, Discovering Witchcraft, III. xv. 65
A flie, otherwise called a divell or familiar
There is also an attestation of familiar angel, in our modern sense of guardian angel, dating to 1460.
From this, it seems clear that the word familiar entered the English language in its usual sense 100 to 200 years before it gained the additional sense being referred to by OP. Thus it is likely a derivation from the prior English, not the original Old French root.
Update: re flie in the quote above.
The same quote is referenced by the OED in sense 5 of the meaning of the word *fly", with flie as an obsolete spelling of the word:
A familiar, from the notion that a devil was accustomed to appear in the form of a fly