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?)