One of the more complicated topics in SEO is internationalization, geo, languages, and so on. It is really fascinating especially when you get into all the rules around spam.
John Mueller clarified in a Google Webmaster Help thread that you can use the original language of your reviews on a different language web page. For example, if your product reviews are in English, you can post them in English on your French version of that product page. In fact, Google wants you to do that over machine translating them and posting the machine translated version of them.
So when you post them in English on your French page, it is okay to add a button to translate them using Google Translate or something similar. This is assuming Google cannot access that machine translation and the user is aware it is a machine translating the original review which was written in English.
Here is the quote from what John send:
Just to address the open question regarding international sites: it's fine to use these reviews on the different language versions of your pages, if they're equivalent pages across languages. I'd recommend making sure that you have the hreflang connection between these pages set up properly, so that we show the appropriate version in search. Also, if you're using computer translations for the reviews (I don't know if this is the case here), please make sure that the translations aren't indexable (automated translations are considered automatically generated content, which would be spam). Showing the original review + providing a JS widget to translate them is fine.
Forum discussion at Google Webmaster Help.