Are they elite in that they can fight in conditions that would break the average military soldier? Probably so.
This is, in technical terms, bullshit. Please don't take offense, there are lots of varieties of bullshit in all branches of military. This is an image created to use as a recruiting tool. Any professional soldier in any professional army is going to have the mental strength to tackle any environment.
Military culture is based in abuse and endurance, and this means elite units get more if both. And this can be a good thing. Wtshtf, you need to know you can push through whatever is in the way. Take a random maintenance company out of the army, put them through seal school, and you will have a seal platoon and some dropouts and casualties. Most of the dropouts will be the ones chosen to drop out by the instructors. (If you don't know what I mean by chosen to drop out, I encourage more research.) My point is knowing how to gut your way through obstacles is going to be covered in basic training of whatever form. Further instruction is a difference of degree, sold as a difference of kind. There is a point of diminishing returns.
FFL is basically the French version of Marines. Light infantry, plus extensive PR. But at least Marines get a better looking dress uniform. Seriously, look at the PR, and show me the difference.
If you are determined to go this route, crossfit is a fine starting point, but honestly, the PT wasn't the hard part of basic for me. It was the soul crushing exhaustion. 16 hours of training, 6.75 days a week, with additional responsibilities to be handled in those precious hours you want to sleep through. For me, it was laundry and 2 separate hours of firewatch.
That's right, train for 16 hours, crash for 1.5, get up and into uniform, stand inspection, clean the barracks for an hour, stand inspection, crash for 2.5 hours, get up and into uniform, stand inspection, clean the barracks for an hour, stand inspection, crash for 0.5 hours, get up and start another training day. 16 more hours of physical training, mixed with long, boring, simple instructions in simple tasks, looking to see who is mentally weak enough to pass out.
I never passed out in class, but I did pass out in drill. Marching in a field, waking up as my face caught the heel of the guy in front of me. That level of exhaustion, every day for 8 weeks. Followed by a relaxing year in advanced school, only working 65 hours a week. No joke, I was pondering with a buddy about the relaxed college like atmosphere when I got to AIT. There were HOURS!!! where were were free to do what we wanted, within limits that were similar to community service restrictions.
That is the training of a maintenance soldier in the US army. I've spoken to plenty of other vets in other services, and the details vary, but it's all the same theme, using the same techniques. Everyone trains as close to death as they can get. By that, I mean, everyone's training schedule runs against the same finite barrier. Every military has an acceptable level of training deaths. US military kills between 1-2k troops per year, most in training accidents. In the first Persian gulf war, we killed 20 guys in training, for every one the enemy killed.
The one thing the scruffy soldiers (FFL, Marines, etc) have going for them is a limited independence. By that, I mean the reason I got out, was I was a cog on a wheel, of a many geared machine. I could be an awesome, sharp, perfect cog, or a lazy, rounded, halfassed cog, and it mattered not at all. I would never be more than a cog. The scruffy soldiers get more indepence of action. More room to improvise, about the level of freedom you give to prison trustees.
So, if you want to go FFL, good luck, have fun, and make the most of it. But, be aware, the diffence between a soldier, an elite soldier, and a scruffy elite soldier (FFL, Marine Recon) is not as big as the recuirters tell you.