Hi there!
I am actually a MBA student at HEC and I would like to say a few things about Indian profiles in our class: 1/ we have Indian guys with both GMAT 750 and 650 - the difference is age (26 vs. 36) and experience (respectively); 2/ the guy with GMAT 650 started his restaurant chain back in India and said he had worked a lot on his essays and other apects of the application.
Actually, the mean GMAT score at HEC is something up to 700 and I would only feel comfortable enough with that score or better. Nevertheless, a good news is that 700 is not that tough. The bad news is that if you can't get something close to 700 then it could be a bit difficult to follow the curriculum... not for you though as you have a goog quants percentile.
Our Indians almost all have beaten the mean and, in my opinion, those in a class are super-smart or so

So some actionable points for you:
1/ improve your GMAT score given your age and lack of super-exciting profile (almost all Indians out there are ingeneers with some good experience both in India and abroad);
2/ make use of your cross-border work and make it clear that you stand out with the skills you have aquired in the US or elsewhere (like leadership, unconventional approach to well known problems together with identifying and framing problems etc.);
3/ don't underestimate essays and put even additional focus on these.
After all, HEC Paris is a very selective school but, to be frank, you will struggle to find a decent job anyway, so think twice before making such an investment (yes or no at all, HEC or INSEAD or LBS or IESE or US B-schools). I am saying that absolutely seriously as there is a trend to hire Masters of Finance from HEC Paris for some juicy jobs as they ask for less, work much harder and know a way more about finance than MBAs do,,,,
good luck!