In the general case I would say it is usually preferable to translate the quotes, even if it is just using an online service. However, when doing so (and this is a practice I've seen done around the site) you should leave the quote from the original language and include the translated one too. That way it helps everyone and people can spot mistakes in the translation if necessary.
I think though generally it should be treated on a case by case basis. A lot of times what makes sense in one question/answer doesn't make sense in another.
You might want to look up these questions for further reading:
In this specific case I don't think it is entirely needed. story-identification questions are a bit of a special case in that they only really exist to help the user who asked the question whereas most questions and answers on the site are more applicable to the larger audience.
In this case as well, as you mention, the OP was looking for the French translation of the work so arguably the French quotes are better here than the English translations.
Further, for a story-identification question the most important part of an answer is that it includes the work name. Sure, it wouldn't be a good answer if it only included the work name but it would still be an answer to the question. As such any further effort is mainly secondary, even if pretty much mandatory.
So, you could go to the effort of translating the quotes and including them but I don't think it is entirely necessary in this specific case.