Old post and I guess you've made your decision but I'll reply for the sake of future visitors.
HEC is the Harvard Business School of France (general population doesn't even know the existence of INSEAD). ESCP meanwhile is 3rd after ESSEC.
Only issue is that HEC is 30 mins from the main city and ESCP is right in the city which should be much of an issue for you if you're serious about your studies.
I'm not sure if non-EU students are allowed to take a gap year(a friend tried and was rejected by the immigration office) but although there aren't many English internship offers, you shouldn't have problem scoring one. Regarding the social life with French, Paris probably has more international than natives themselves. All my friend's who had been on exchange complained how they didn't have any French friends.
I know all foreigners in the grande école program and they have basically all found an internship in France or been able to do a gap year if they wanted. I only know of two exception from the US and Greece who returned back to their home, but they werent really flexible in their internship hunt (no prior work experience but would only accept marketing internships from big luxury brands - supply chain mgmt in the same company wasnt good enough/what they wanted even though they got it offered).
If you are on exchange I guess you rarely have many French friends on any school in France (having been at ESSEC on exchange myself).
MGMAT 1 - 580 - Q36 V33
MGMAT 2 - 650 - Q44 V35
GMAT 1 - 690 - Q48 V38
MGMAT 3 - 680 - Q47 V36
MGMAT 4 - 690 - Q44 V39
GMAT 2 - 700 - Q48 V37