Giving your standings, FFL isn't a good option.
First things first, you have to confide to the French version of the military, learn to speak French, and to use their weapons.
When I did volunteer work guarding private hospitals in Kenya I've had dealings with the FFL. Most I've came in contact to where either from the same shithole I was in, or a European country.
I was a 31B retired as E-5. I got sick of civilian life, I knew a friend who owned a small time security firm in Oregon. He invited me over for some beers one weekend and, the next week I got my Armed Guard Card, if wasn't too glamorous starting out, a lot of boring times.. after a few months I worked Federal sites, mostly small time Social Secuirty offices, a bank and I even got a spot working for the local MEPS.
After a few years, around 07' when I retired I thought there would be no skills that would be good. I never thought about becoming a cop, or even working security.
Anyways, fastforward a few years, the government liked us so much they offered some Dept. of Homeland Security contracts.
After my last year, I started doing private protection. Not the shitty celebrity body guard shit, I'm talking about armed asset protection.
Armed asset protection and private armed contracting is where the money is. Unfortunately most companies don't offer these, they are niche jobs. They pay very well, you don't get dumbass people running through, and you can get great benefits.
Since you're Airborne Infantry, you'll definitely be eligible for some contracting companies, I'm not talking Black Water tier, but moving valuables for rich old men pays the bills.
Don't waste your effort and time joining an organization where you'll be re-deployed into some shithole trying to win "hearts and minds". Especially fighting for someone who's values you don't believe in.
If you have any further questions, please let me know. I'd hate to see the kind of talent like yours go to waste.