Hi HK, being an Indian male with a 710 GMAT is a rough spot to be in. Honestly you would need to make a concerted effort to add 20 points to that or go to a less prestigious but still well reputed School (than INSEAD.)
You were right to apply to HEC in the sense that the average of 690 and 710 is what would make you viable as an Indian. However it is a global program and so if you don't have a lot of international experience that's going to be a real demerit.
I will share with you that when I do ding analysis for most Indians their essays lack any real emotion or depth of feeling and it makes you feel like you're not getting to know them. They tend to be very quote professional oriented which is honestly the absolute wrong way to approach this project.
You want to make the adcom feel something, like you and root for you. That means you have to talk about feelings thoughts your inner monologue etc. Introspection is key.
So that might give you some sense about why you did not get any traction with HEC... I could be completely incorrect but that's what I see like 99% of the time.
I think you should apply to round 1 programs with January and take if you're interested in European schools. IMD, Erasmus, SDA... maybe throw the dice with ESADE R4.. apply to January intake Canadian schools such as Ivy, Queens... this might not be a bad option because it comes with a 3-year work visa. Consider ESMT for cost reasons...or buckle down on the GMAT and apply to US schools early action round. The early action round part is important.
https://mbaprepcoach.com