When citing a French citation in the original, should the guillemets (angle quotes) be changed? What about punctuation order?

Solution 1:

If you are quoting a chunk of French then it is no longer an English document: it is a mixed English and French document. For the French parts you should follow French rules, and for the English parts, English rules.

You should no more change the French punctuation rules to correspond to English punctuation rules than you should change n’existe pas to ne pas exist to correspond to English word order.

Solution 2:

1.) If the French quote, itself, is going to be immediately translated: leave it as it was originally punctuated in French.

English language readers will know from the quote's English translation what the guillemets (angled quotation marks) are. It provides them an interesting example of the difference between English & French language punctuation.

2.) If the French quote, itself, is not going to be translated: do whatever you think helps English language readers best to understand it.

Most likely that would be to offer an English translation of the quote, anyway - even as a footnote placed somewhere else in the text. So, you would keep the original French punctuation in the French quote in this case, too.