In France, it is common for academic publications, professional bodies, and universities to all have their own preferred styles of citation. Because of this diversity of potential styles, the use of Zotero is recommended for citation management. The tool will allow you to export your citations to any number of French styles.
In North America, citation styles tend to be more standardized: the most common styles in Social Sciences and the Humanities are APA, Chicago, and the MLA. These styles were created for an English-language audience, so writers in French have to make editorial choices as to how they adapt these styles for French-language writing.
RECOMMENDATION: The Translation Bureau of the Public Works and Government Services Canada maintains a website of preferred "styles" for Canadian governmental publications. I recommend that students and faculty follow these guidelines for consistency. The Translation Bureau's website gives advice on using <<Quotation Marks>> or Italics as well as how to format <<Quotations within Quotations>>.
Consistency and understandability are two important aspects of citation styles. When in doubt, talk to your professor about their preferred method when it comes to translating North American styles into French.