Translating effet by “efficiency” or “effectiveness” would narrow down the meaning somewhat. Efficiency and effectiveness relate to the quantification of useful consequences resulting from the use of the machine, relative to the effort that went into making the machine work. Effet in French, like effect in English, more broadly covers the consequences resulting from the use of the machine as a whole.

In the preface by Navier, Girard and de Prony, I think effet means what physicists today call work (travail, which is the term introduced by Coriolis in this very book and used by physicists today).

While effectiveness is basically work divided by input energy, this is a social consideration in that only certain effects are considered useful. Coriolis’s book is about physics, and analyses physical measurements: work, energy, etc. I would say that effect is as effective a translation as any, and efficiency or effectiveness would be wrong — if the author had meant to write efficacité in French, he could have done so.

If you need to choose a word in a language that isn’t etymologically related to French, the gist of the word effet is, what happens when the machine is used. It doesn’t carry any implication of usefulness. A secondary consideration for translation would be to tie the use of the word to physics vocabulary, but this is somewhat difficult: readers in Coriolis’s time may have understood a physical meaning of the word effet, but modern French readers don’t, so even a translation into modern French would have to choose between respecting the everyday language meaning (so retain the word effet) and choosing a physical term (which could be travail [work] or possibly even energie). I would go for the everyday meaning, i.e. keep the title as it is.

Both “Efficiency” or “effectiveness” add some kind of judgment of value (i.e. quality, performance) while the French “Effet” is neutral.

Both “Effet” and “Effect” are just about observing and measuring the results of what the “machine” produces without judging whether it is better than something else or not.

ADDED Dec. 6 to try to address the OP’s comment to my original response (see far below for my original, unedited response):

So it seems that you want a suitable synonym for « Effect » that wasn’t specifically used by physicists to describe machines and their power prior to Coriolis’ innovation. Maybe that’s why Coriolis arrived at the seemingly curious choice of “Effet” because he didn’t want to be accused of using/borrowing a “better” word already used by his predecessors/competitors, and maybe it would be wise to accept/respect his choice and stick with “effect.’

But if you’re still searching, I would offer some final suggestions based on the “produire/to produce” sense of the word “effet”: “Ce qui est produit par une cause.”
So working with “to produce/product,” you could get to “the productivity of machines,” but like ‘Efficiency’ and ‘Effectiveness,’ ‘productivity’ could still imply a value judgment, although perhaps a bit less than the two “E” words.
To remain completely neutral using the “product” sense of “Effet,” you could perhaps use:

“the production capacity,” “the production capability,” or “the production potential” [of machines].

(Finally maybe adding “potential” before “productivity” [or even before “efficiency” or “effectiveness”] would help resolve the value judgment issue and retain neutrality in the translated title, i.e., “Calculation of the potential effectiveness/efficiency/productivity of machines.”)

(Original Response)

The more I read your question, the more I understand your desire to replace/”change” effect in the English title.
There’s a meaning of effet, the French noun, that is “puissance transmise (par une force, une machine)” in my Le Robert-Micro and therefore, I think “Power” would be a suitable replacement that would convey in English both the (^)effect sense and the above physics sense conveyed by effet in the original French title.
(^)(Effect arguably could mean Power in the sense that:”She has an effect on me/She has a power over me)

(BTW, in checking the meaning of puissance, I actually found force and efficacité (!efficiency/effectiveness!) as synonyms under definition #3 (still in my Le Robert-Micro), but I agree with others that efficiency/effectiveness would be changing the meaning and adding a value judgment. “Calculation of the power of machines,” however, would seem to maintain the neutrality found in the French title [and it would work for horses, too!]).