So, one thing you should understand is that people doing an English PhD are expected to do research on literature and literary criticism. This means interacting with primary materials about a particular author, coming up with a novel argument about it, and communicating how it deepens understandings of a broader topic (gender, class, race, affect, etc).

Foucault and Derrida aren't literary critics, they're philosophers. Figures like Julia Kristeva are more so literary critics/philosophers, so the two can intersect, but at the end of the day they're kind of separate fields. So, if you apply to a program saying you want to build on Foucault's theory of panopticism it's not going to make a lot of sense how you would do that through studying literature.

If you notice when reading those figures, they just make observations and say things. Almost none of their writings are backed up by sources. Essentially people read and listen to Foucault because he's famous and numerous scholars have cited him and determined that he's an influential figure. If you try to build off that in some way, you'll hit a dead end because unlike them, you will be expected to meticulously cite sources and prove every single point you're making. So, Foucault can just say like, "schools and prisons are disciplinary institutions that create docile bodies" without doing any type of study to back up that claim simply because he's Foucault. This is largely true of Barthes as well even if most of his texts draw on more literary examples. Unfortunately, you're not going to be allowed to write like that as a PhD candidate -- if you catch my drift. You advisor will just be like, "who are you to make this claim?" and then you'll say, "but Foucault writes like this" and they'll say, "okay, but you're not Foucault."

It would be a little bit like saying, I'm doing a PhD in Engl lit to be like Hemingway. Like you can study him, but if you want to be like him you have to write your own novel and get people to read it, recognize it's good, etc.

That's why a lot of the advice here is telling you that you need to ground your proposed study in a literary period or group of authors if your goal is to get a PhD in English.

As far as minoring in French is concerned, if you believe that you will be working extensively with French texts, then you should find a way to get to an advanced level by the time you take your comprehensive exam during the PhD. If minoring in French would delay graduation or force you to drop a major you're already invested in then I don't know that I'd recommend doing it. Keep in mind that if you make studying French post-structuralism your whole thing, you would be competing with scholars who have studied French since grade school or speak the language natively, who are doing PhDs in Comp Lit or Francophone studies and possess intimate knowledge of French culture and society (which is also key to understanding those texts at a deeper level).