The PDF article^* linked in hunter’s comments to the question was right on point. It considers three hypotheses on the origin of French partitives. I will just mention them here so other members can form an idea ahead of reading the article itself.

1. The Deleted Quantifier Hypothesis: According to this, French partitives derive from a form consisting of: a quantifier + de + noun. The historical stages of the development are supposed to be exemplified by: asez de vin > assez du vin > del / dou / du vin > du vin. That is, the quantifier dropped out while the definite article came in and stayed but without contributing its meaning to the modern partitive. (That is, du vin is some wine, not some of the wine; i.e. its reference is to a bit of unspecified, rather than specified, wine.)

2. The Prepositional Object Hypothesis: According to this, the partitives derive from their occurrences in constructions like Il boit du vin. This construction is supposed to be syntactically ambiguous because boire may be a direct transitive verb taking the object du vin or an indirect transitive verb, i.e. boire de, taking the object le vin.

3. The One-Sided Preposition Hypothesis: It is so named because, according to it, de is a preposition in its relation to the noun it governs but not a preposition in relation to its external context. The author tries to motivate the hypothesis with a paradox that trips up other hypotheses and even to provide historical evidence.

I have not thoroughly worked through the article yet and so may not be presenting it fairly.

You may, however, notice that the author’s own hypothesis in fact describes what modern partitives are: De is not a preposition externally (which is why du vin may serve as e.g. the subject of a sentence), but a preposition in relation to le vin (the partitive sense being ultimately that of X being part of Y). Thus, we may say that it is the “no-derivation theory of the derivation of partitives,” or the view that a one-sided preposition should be accepted as a more or less primitive grammatical category. For this, I believe, she appeals to non-French precedents. But I don’t know that she can rest there. You may simply ask how in those other languages such a thing as a one-sided preposition came to be? I think the plausibility of her thesis may ultimately rest on how fine or not fine you, the reader, are to multiply primitives

Notes

* “From preposition to article – The grammaticalization of the French partitive”, Anne Carlier, University of Valenciennes