English and French pluperfect constructions are not descended from a common ancestor
The English pluperfect tense (along with all the other composite tenses made with "have") is not what is called "genetically" related to the French past composite tense (or any of the other composite tenses made with "avoir"). The use of "genetically" in the preceding sentence might be confusing; if it is, here is an explanation. It doesn't have anything to do with genes. In historical linguistics and etymology, words or structures in different languages are said to have a "genetic" relationship, or just to be "related," only under very specific circumstances.
First, the two languages must descend from a common ancestral language. This is true for English and French: they have a common ancestor that is reconstructed as Proto-Indo-European.
Second, the words (or structures) that we are comparing must come from a common source word (or structure) in that ancestor. This is not true for have and avoir. If we look these words up on Wiktionary, it says have is descended from Proto-Indo-European *keh₂p-, while avoir is descended from Proto-Indo-European *gʰh₁bʰ-. These are completely different roots.
There is also a third requirement: the words must have been continuously present in each language since the common ancestor. Pairs where one language has borrowed the word, such as English infant and French enfant, do not count as "related" for the purpose of historical linguistics. This is kind of an unintuitive use of the word "related," so be aware that etymologists generally use the word differently from the normal, broader definition. Another term that generally means "genetically related" is "cognate."
But the languages are believed to have influenced each other in this area
Now that that's said: although "have" and "avoir" are not etymologically related, it is generally believed that the use of the cognates of "have" in the Germanic languages influenced the use of the cognates of "avoir" in the Romance languages (and vice versa). If you look at this map on the World Atlas of Language Structures, "The Perfect," you can see that perfects formed with the verb "have" are generally rare (these are the languages coded as "From possessive"). But there's a relatively large amount of languages with this construction clustered near each other in Europe.
Unfortunately, I don't know the details of how and when this construction developed, and which language group could be considered the origin of it.
So while this similarity does not in the end show that French and English are related to each other, it does provide some evidence that they developed in the same area and influenced each other historically.