French's 'ne explétif' in English?

Cannot but behaves as a set phrase in English:

Idioms

2. cannot but, have no alternative but to:

The double negative with but is used to convey an ambivalence toward the inescapable outcome, and adding the word help to form cannot help but, seems to multiply the emotional intensity of that ambiguity. In 1892, The Foundations of Rhetoric pp. 161-162 compared the expressions "Can But" and "Cannot But"

"Can but" brings before the mind only one possibility; "cannot but" suggests two opposite courses, but affirms that in the case in hand only one of these is possible...

"You cannot but realize that you are" means you cannot help realizing that you are, you cannot believe that you are not.

"You can but realize that you are", means you can only realize, you cannot do more than realize, that you are...

"He could not but speak" is equivalent to "He could not help but speak," Help...is tautological.

In 1846, the Horatii Tragedy uses the phrase cannot help but, in a dialogue to evoke the emotional compulsion of fear:

Horatia: What, art thou weeping?

Mysis: Yes, my lady.

Horatia: What ails the? What's amiss?

Mysis: Nay, I cannot help but weep, my lady.

Horatia: But tell me thy sorrow, good wench ; peradventure I may comfort thee.

Mysis: Why, to be plain with thee, sweet mistress ; I am weeping about Bubo...I have bethought me of so many risks, and perils, and dangers, and mischiefs, the which poor Bubo may run against, I cannot help but weep.

Again in 1846, The Christian expresses emotional ambivalence in a religious conflict:

I cannot think, or feel, or talk, or act on this principle at all. My thoughts, my feeling, my talk, my actions, go all on the opposite principle of liberty. I cannot help but feel that there are some things which deserve blame, and others which deserve praise. I cannot help blaming myself, if I do wrong, and I cannot help praising or approving myself, if I do right. And I cannot help feeling that there is a difference between right and wrong.

Beuachampe in 1856, uses the expression to capture an internal conflict with fate:

I can not help but tell it. An instinct, which I dare not disobey, commands me; and truly, when I think of the instinct which told me that you would come--made you known to me as the avenger from the first moment when I saw you--and has thus forced you, as it were, in my own despite, upon my fearful secret--I almost feel as if there is a divine, at least a fated compulsion...

Almost every use in written English was in the context of emotional ambivalence, conflict or compulsion:

In 1892, A Doctor of the Indiana State Medical Association expressed his ambivalence while confronting a prevailing medical opinion on the treatment of pelvic peritonitis:

I have seen so many of these cases operated upon, so many that had previously been tested with electricity and not made better, but made worse, that I can not help but believe that it is good doctrine, when you have a case of recurring attacks of pelvic peritonitis, "hands off" with your electric machine.

In 1987 hearings on the Alaska Arctic National Wildlife Refuge, a representative expresses emotional ambiguity toward the evidence presented by a witness:

I can not help but note that when you look at the rewards that might come from development on the North Slope in terms of total gas and oil that might be discovered on the North Slope or in ANWR, you use the lowest possible prediction. And when you talk about potential damage, you use the highest possible prediction.

Interpretation: I must note, but I can't believe I have to note, such an obvious bias. The same interpretive formula is applied to I cannot help but think:

I am compelled to think, but I cannot believe (or like that) I must think.

The expression I cannot deny but that, generates the same sense of emotional ambivalence toward the denial:

I cannot deny, but I cannot believe (or like that) I cannot deny.

Conclusion:

Fink's thesis is that this use of but (and especially help but) behaves like ne explétif, implying a subtle emotional distance from an inescapable conclusion. When the OP eliminates both negatives of the double negative, that emotional ambivalence is incorrectly removed.

I cannot help but think, is similar to I think in meaning, but they are definitely not identical expressions.

I cannot deny but that is similar to I cannot deny in meaning, but they are definitely not identical expressions.

dictionary.reference.com

books.google.com/ngrams/graph