Never fear, I'm going to endeavor to answer this question myself. Having looked at every souce I could possibly find that mentions Éléonore Duplay, I must observe that every secondary source that claims she was a student of Regnault's (and cites a source for this) cites the same memoirs, by a certain Albertine Clément-Hémery, who claimed to have been a fellow student of Éléonore's in Regnault's atelier de jeunes filles. No other primary sources mention that Éléonore studied painting, which means that the only real evidence that we have are these memoirs and her alleged self-portrait (which obviously had to have been painted by someone with some technical knowledge).
Now, the chapter of these memoirs concerning Regnault's studio has been published on Gallica and I've been able to read it - and translate the relevant parts for you - and there are a few things I notice about it that make me rather suspicious. The first is that Clément-Hémery spends the whole chapter calling Éléonore Eugénie. Now, since she calls nearly all the other students by their last names, this point alone doesn't necessarily invalidate her testimony; it's quite possible that she didn't know or didn't remember - since they would likely not have been on a first name basis - Éléonore's first name and it's clear that she only refers to her by her first name in these memoirs to keep the reader in suspense as to her real identity, which isn't revealed until the end of the chapter.
Of course, that's not all. Aside from the author's overactive imagination (aside from the fanciful incidents depicted below, Clément-Hémery also informs us that she could see Charlotte Corday and Antoinette pass beneath the windows of the studio on their way to execution, which, as Lenôtre points out, is an impossibility), she's also under the impression that Éléonore was blonde, which tends to tip me off right away that either she had never actually met her or she associated with her so little that that is the kind of detail she could have forgotten. She also thinks that Éléonore and Charlotte Robespierre were friends, though she admits to having that one on hearsay, so we might fairly let it pass.
As for the rest, let me put the relevant text in front of you, and then I'll tell you my hypothesis.
( A Studio... )
So here are my thoughts: Does this chapter prove absolutely, even in conjunction with her alleged self-portrait, that Éléonore really studied under Regnault? No. To really affirm that absolutely we would need other outside evidence. Perhaps it exists somewhere; apparently someone wrote a thesis on Regnault (which is unfortunately only available in a hard to access art library in London) which lists forty-one of his female students, but I don't know if Éléonore is listed there and even if she is, the source might once again be Clément-Hémery.
However, I'm not convinced that it disproves Éléonore's art student status either. If you leave aside all the obviously made up incidents (I haven't read every session of the Jacobin Club, but I'll eat my hat if any of them turns up a denunciation of Regnault for wearing a beard) and the errors mentioned above (name, hair-color, etc.), it's not at all impossible that Éléonore and Clément-Hémery were in the studio at the same time.
Let me explain my reasoning by starting from what we know. First, to clarify, it seems likely enough that Clément-Hémery really was a student of Regnault's; several of the students she mentions are known to have been Regnault's students because they went on to have careers. It's theoretically possible that she invented the whole story out of whole cloth, but let's assume for the sake of argument that she didn't - especially since these kinds of memoirs usually have a least a grain of truth in them. Clément-Hémery tells us herself that in 1793-1794, she was 14 and then 15 years old, which would make her a full decade younger than Éléonore. It seems unlikely that they would have had much to do with each other, especially if Clément-Hémery and her friends were the bunch of giggling aristocratic idiots she depicts them as - which I have no reason to doubt. It's quite likely that they would have taken no notice of each other.
Now, at a later point in time, it's quite possible that someone who did know Éléonore or who was at least aware of her presence in the studio, mentioned to Clément-Hémery that she had been there - perhaps even in a similar conversation to the one depicted at the end of the memoirs where "Eugénie"'s identity is revealed. That would explain her knowledge of the rumors regarding Éléonore (oddly, this isn't the only source to allege that Éléonore and Robespierre were secretly married with Saint-Just as a witness, as absurd as the idea might seem) as well as certain errors, particularly regarding her appearance. If this hypothesis is correct, then Clément-Hémery filled in the traits she would have imagined Éléonore to have had and added details on the "Terror" to make her account more interesting.
These memoirs ring most true when Clément-Hémery talks about knowing nothing about politics and about these years being the happiest of her life - in those moments they recall Élisabeth Le Bas's memoirs, and if Élisabeth Le Bas, while being married to a Conventionnel and living in the same house as Robespierre could be as little affected by political questions as she seems to be in her memoirs, how much more true is that likely to be for a 14 year-old boarding school student who, even as she peppers her account with your standard Romantic fantasies on the "Terror", admits to having been ignorant and sheltered?
In short, my supposition is that Clément-Hémery and possibly Éléonore studied under Regnault without interacting with each other in particular, that someone later informed Clément-Hémery (rightly or wrongly) that Éléonore had been in Regnault's studio in 1793-1794, and that Clément-Hémery then made up everything in her memoirs concerning Éléonore and anything political. At least part of what she recounts of herself and her circle of friends may be true, as well as some variant of the final conversation presented here, but that's about it.
EDIT: It should also be noted that neither the famous passage about Éléonore's believing she was loved when really she was feared nor anything about her fellow students' supposedly explicitly calling her Mme Robespierre are anywhere to be found in these memoirs. The first is a summary by Lenôtre, the second, while I supposed it could be considered to be implied if we are to believe that some of the students thought that Éléonore and Robespierre were married, simply isn't there. (Which, btw, makes Hilary Mantel's statement that "'Eléonore thought she was loved,' said a fellow-student, 'but really she only scared him.'" doubly erroneous, since not only did Clément-Hémery never say this, but even Lenôtre's summary isn't referring to Robespierre's relationship with Éléonore, but to the fear of Éléonore among her fellow students alleged by Clément-Hémery.)