The phrase "Man will believe anything, as long as it's not in the Bible" is attributed to Napoleon on many sites but there are no further details (date, context,etc.) available, nor a trace of primary sources.
It's difficult to prove a negative, especially when the purported quote is a translation with no reference to the original. But signs point to no.
I tried searching for a possible French original and found nothing, but there are so many possible ways this could have been said that the only word that is very likely to be present is “Bible” (spelled the same in French). Most of Napoleon's writings are available in searchable form online (but not all of them, and it's possible that he could have said it and not written it). I search for occurrences of “Bible” in Napoleon's writings on Gallica (this includes books written by others that include large amounts of quoted text), and searched for "Bible" throughout all the documents (which have some overlap) and found nothing remotely like this sentence. The OCR quality is mostly good, but a few are bad, so I could have missed something.
Of particular interest is the Dictionnaire Napoléon, ou Recueil alphabétique des opinions et jugements de l'empereur Napoléon Ier (“Napoleon dictionary, being an alphabetical collection of the opinions and judgements of the emperor Napoleon I”), which jumps from Bessières to Bichat (no bible) and from Crevier to cuirassiers (no croire or croyance or other word from the same family, and I can't think of a word with another root that would be plausibly translated by “believe”).
Searching in English, it's notable that on Google Books, there are no occurrences of
"will believe anything as long as" "bible" before 2000. The earliest hit is an article published by the Creation Research Society which presents the exact quote as a “famous quip”, without attribution. “Bible Counseling” by Mallet et al. 2003 is the earliest book I can find that attributes the quote to Napoleon. Like all of its successors, it doesn't provide any specific reference.
(Note: Google Books links may or may not work for you due to Google's restrictions. Repeating the search should work, but some results may be region-restricted.)
In conclusion, this seems to have been made up and passed around by English-speaking Protestant apologists.
(I have to say, though: I can understand making up a quote like this, but why on earth attribute it to Napoleon?)
To a bit more history here, there's a 1998 book Soaring and Settling by Rita Gross, which has a different take/version (p. 43):
I am just as frustrated that many Caucasian Buddhists, reasonably sophisticated in their assessments of certain elements of Christian tradition that are woefully out of date, will believe anything as long as it is said by a Tibetan lama.
I suspect it's this passage or something similar that was the basis of the post-2000 broader but similar pronouncements.
Regarding Napoleon, he generally found Catholicism useful, but Protestantism not so much. So it's quite unlikely he would have said something that simplistic about the Bible. On the other hand, Napoleon was/is more often demonized or derided in Protestant circles, which is a more plausible reason why the quote might have been attributed to him in such circles.
There have been similar phrases uttered by many different people. Very often, it is said by religious leaders attacking atheism, especially by creationists attacking Darwinism.
Attribution to Napoleon goes back a long way. Here's a book from 1883. Note that the anecdote is uncited, and told by an anti-Darwinist. Very probably apocryphal.
It is related of Napoleon that one day his friend Duroc was reciting to him a marvelous story. Duroc was a skeptic, indeed more than that - an avowed unbeliever. As he ended the improbable tale Napoleon answered "Some men can believe anything but the Bible."
Here's an earlier example,from 1868, attributing the remark to Napoleon speaking of Duroc, without context, and without a cite.
The earliest example I've been able to find of the phrase itself is in a medical journal dated July 1852. No attribution to Napoleon.
It is an old observation that complete scepticism in religion is often allied with extraordinary credulity in other matters; and we have a remarkable verification of this in the present time, in the authors of 'Man's Nature and Development' of one of whom it has been not unaptly or untruly remarked, that "she will believe anything that is not in the Bible."
Napoleon born: 1769
First known attestation: 1716
Conclusion: NO! (Not the first at least.)
This Learned Divine, said he, is a very strange Man: He believes every thing but the Bible.