In the old days, my favorite text of Foucault was the beginning of the Archaeology of Knowledge (online here), revised from his “Réponse au Cercle d’épistémologie”, published summer 1968 (o pregnant time!) in Cahiers pour L’Analyse, the original of which is separately translated in Essential Works vol. 1. There is a nice summary of the original and its historical context here.
At this time, Foucault and Althusser were both working toward what has been called a rationalist philosophy of the Concept related to the work of Jean Cavaillés and Georges Canguilhem, in contrast to then popular existential/phenomenological philosophies of the Subject. (See Knox Peden, Spinoza Contra Phenomenology: French Rationalism from Cavaillés to Deleuze.)
The Epistemological Circle that Foucault was responding to was a group of Althusser’s students interested in the philosophy and history of science, as well as structural Marxism and Lacanian psychoanalysis, who had asked Foucault a series of methodological questions. Althusser was something like the dean of France’s most prestigious university. He had actually written his dissertation (which I have still not seen) on the Concept in Hegel. By this time he was in high anti-Hegelian mode, as was Foucault.
Foucault himself acknowledged considerable debt to his Hegelian mentor Jean Hyppolite, who translated the Phenomenology to French. Hyppolite read Hegel as focused more on discourse than on subjectivity. His 1952 Language and Existence, referred to by Foucault as “one of the great books of our time”, argued strongly for the importance of language in Hegel. (It was also very favorably reviewed by the young Deleuze.) Foucault had written a thesis on “The Constitution of a Historical Transcendental in Hegel’s Phenomenology of Spirit” under Hyppolite in 1949.
There is more good historical background in James Muldoon, “Foucault’s Forgotten Hegelianism”. While I don’t endorse, e.g., Muldoon’s remarks on Hegel and free will, his suggestion that an identification with certain specifics of Hyppolite’s reading of Hegel — particularly the attribution of a strong “totalizing” impulse — contributed significantly to the anti-Hegelian turn of Foucault and others is quite interesting.
Though I don’t recall this from his translated works, Hyppolite apparently both saw a strong element of totalization in Hegel and strongly rejected it, while continuing to identify as a Hegelian. (Previously, in absence of more specific evidence I had surmised it was mainly a reaction against Alexandre Kojève’s reading that drove the French anti-Hegelian turn. Muldoon also says Hyppolite’s reading was initially welcomed as a contrast to Jean Wahl’s more phenomenologically oriented 1929 book on the unhappy consciousness, which apparently also contributed to French perceptions of Hegel as subject-centered.)
In any case, the Hegel whom Foucault, Althusser, Deleuze and others famously rejected in the 1960s was identified as the proponent of a totalizing historical teleology of the Subject. Each of the three components of this was independently strongly rejected — the subject-centeredness, the historical teleology, and the totalization. I still agree today that these are all serious errors that should be rejected.
However, Hegel read in a broadly Brandomian way is utterly untouched by this criticism. There is no historical teleology at all in what Brandom calls Hegelian genealogy (so a fortiori not a totalizing one), and there is no subject-centeredness in the analysis of conceptual content. Subjectivity is never invoked as an unexplained explainer. Brandom’s exposition of the Hegelian critique of Mastery offers us a Hegel utterly opposed to the kind of totalization attributed to him by Foucault, Althusser, and Deleuze.
Foucault presented a long list of forms of discontinuity that should be attended to in the history of ideas. Each of these could be analyzed in Brandomian/Hegelian terms as a determinate negation.
I agree with Foucault that it is very important not to take the simple continuity of a tradition for granted. In principle, such things need to be shown. However, I still think defeasible assertions about “traditions” and other such unities that should be questioned can play a useful role in historical discussion. (See also Ricoeur on Foucault; Structuralism; Structure, Potentiality; Difference; Identity, Isomorphism; Univocity; Historiography; Genealogy.)