Hi gpderivatives,
First off, a 650 is a solid score, so it could be enough to get you into HEC Paris. The Q38 might be seen as a bit of a 'red flag' though. That all having been said, there are a number of different 'pieces' that go into a Business School application, so you would likely find it beneficial to speak with an Admissions Expert about your overall profile. There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/If you do choose to retest, then we have to examine how you were studying for the Quant section before. Once you've decided on whether to retest or not, you should post back here (or you can PM me directly) and we can talk through your study options going forward.
GMAT assassins aren't born, they're made,
Rich