Even if you assume that the law says you can carry ... and you get fired ... what is going to be your relief? Nothing. Look up "at will employee"
This. Unless you are in a union you're out of luck.
Not quite correct - but ....
Sure you could sue them (or file some sort of EEO complaint with the La state folks) for wrongful termination, as well as apply for unemployment benefits under the same theory. There isn't likely to be an attorney willing to take the case on a contingency basis, so you will have to commit rather large amounts of money to the effort. And other than recovering your costs and back salary from date of termination to date of ruling, I doubt you would see much more in the way of damages awards.
You could ask the court to reinstate you, but would you want to go back to work there (other than the first day so you could twell them how you feel and quit)? Claiming reprisal is easy but proving it is difficult.
More important, from where I sit well outside the immediate issue, is that the OP is now "on record" with his boss (2A supporter that he might be - right up until his own job is on the line). I'm willing to guess that the company policy says they can ask you to unlock you car and poke around inside any time they want. Those policies almost always say refusal is grounds for termination - which can be avoided by quitting on the spot.
Sometimes it is better to limit 2A conversations at work to hunting and what that crazy Ted Nugent has gotten himself up to this time. Maybe go way out on a limb and talk aout playing IDPA/IPSIC. But personal self defense? That's a personal matter. Don't talk about that or what you and your lady did last night. It sucks to be caught in that situation, but sometimes it is discretion and continued employment or ....
stay safe.