What about the case of "croire à"

Bonjour Andy,

The verb croire tends to be used transitively, that is, with a direct object. 

Normally the form is croire que + indicatif mood (vtr + conj)

But to express "to believe in something" uses croire à.

Eg.   Mon fils croit encore au Père Noël --> My son still believes in Santa.

To take your proposal "Elle croit à une mauvaise blague" --> She believes in a bad joke.

Is this what you have in mind?  --  because immediately above is the translation.

Bonne Journée

Jim

@Celine. The sentence comes from Assimil. I just confirmed from reverso that this is not an unusual formulation to find in the wild in the original French, was not using it to translate.

@Jim No, the lesson gave it just as I translated above. She has received bad news and thinks it is a bad joke ("croire en" for "believes in" was taught separately, although I see "croire à" is equally valid). Here are a few random samples from reverso: "Il croit à une bande organisée" and "Elle croit à un rencard" Both of these are confirmed, by looking at the surrounding sentences, that they mean "___thinks it's a ____" (organized gang/date, respectively), as in "is under the impression that it is ______."

In most online translators non-standard usage can make an appearance and then be repeated. One of the problems is that the online translators give an answer for any gibberish put in, and may have been programmed to ‘translate’ a misused phrase or structure in a particular way. As is the case for any model, or tool, they are sometimes useful, but all have limitations and flaws. 

To be ‘fair to online translators’,  doing a two-way translation - French-English-French - in reverso and in DeepL ends up at the sentence “Elle croit (or pense) que c’est une mauvaise idée” for “She thinks it’s a bad idea”, in response to the initial phrase ‘elle croit à une mauvaise idée’. 

At least in DeepL with its option selector “elle croit à une mauvaise idée” did not appear on the reverse translations list - a strong hint that it is not standard. I didn’t get options in reverso, or maybe I don’t have access to that function.

Human translators are not perfect either, but I know which I put more faith in at this stage of development !

https://progress.lawlessfrench.com/online-translators-the-good-the-bad-and-the-ugly-translations?

I think Andy was quite clear that he wasn't using an online translator - reverso also gives you examples of texts that have been translated by human translators.

You can find lots of examples of "croit à une blague", or variations of that, using google search, so it does seem to be a valid option.

For example, from Le Monde:

Comme d’autres lauréats du Nobel avant lui, lorsque Jean-Pierre Sauvage décroche son téléphone en octobre 2016, il croit à une blague. Pourtant l’annonce téléphonique est bien réelle : le Français a été choisi par l’Académie royale des sciences de Suède.

https://www.lemonde.fr/sciences/article/2022/04/27/les-molecules-ces-belles-machines-vivantes_6123883_1650684.html

@Alan and @Maarten--Thank you, Alan. Maarten, in addition to what Alan mentioned, as I have basically said twice now, it is actually what is taught in Assimil directly, which, to be clear, is a book for learning French that is written and updated by French native speakers, and has nothing to do with online translators, which I have never relied on as a source for anything, as I understand the unreliability of doing so.

https://www.cnrtl.fr/definition/croire

III.A.2. [Le subst. désigne une chose] Croire à qqc.

c) Penser qu'il peut s'agir de quelque chose;

I think we can see from this definition why "Elle croit à une mauvaise blague." is correct, but the example Maarten looked at, "Elle croit à une mauvaise idée." might not be.

@Alan, thanks, that helps confirm what I noted above about both examples seeming to mean "is under the impression that it is ______." It also helps to know that this is not too mainstream of a usage.