I will try and make this as easy to understand as possible.
First, the courts determine the constitutionality of statutes (laws). In doing so, they typically choose from 3 different levels of judicial review -- rational basis, intermediate scrutiny, and strict scrutiny. Rational basis is the lowest level of protection. U.S. Supreme Court Justice Scalia plainly asserted that this level of review cannot protect a fundamental constitutional right (e.g. speech, right to vote). The highest level of protection is strict scrutiny and this level is reserved for the protection of fundamental rights. Post Heller and McDonald, state and federal courts have refused, in almost all cases, to give the fundamental right to keep and bear arms the highest level of protection and have usually assigned intermediate scrutiny or other rights infringing analysis.
In Louisiana, the state's Supreme Court has made the current right to keep and bear arms provision meaningless because they assigned it the lowest level of review -- rational basis. The proposed amendment requires the Louisiana courts to accept the right to keep and bear arms as fundamental and raises the necessary level of review to the highest level -- strict scrutiny. In short, the proposed amendment requires the right to keep and bear arms to be viewed by the courts under the same protections as your right to free speech and right to vote -- this has never been done on the state or federal level.
Additionally, the proposed amendment removes the legislature's constitutional authority to ban concealed carry. Very few states have the express constitutional authority to ban concealed carry -- however, 49 states regulate the carrying of firearms. The removal of this provision will protect law-abiding Louisianan's right to carry.
It is also important to note that under the current provision or the new provision -- the legislature will still be able to pass any bill they choose. The legislature, under separation of powers, passes laws. It is the judiciary's duty to interpret the law's constitutionality.
So to your question, how would a law be determined unconstitutional? If an individual decided that a state law infringed on his or her state-constitutional rights, the individual could challenge the law in the court system. Under the new provision, under strict scrutiny, unlike under the current provision, the challenged law would be initially considered unconstitutional -- the burden would be on the state to prove otherwise (under the lesser standards of review the burden is on the plaintiff (the people)). The state would than be required to prove that the state has a compelling interest, that the law is narrowly tailored as not infringe on the rights of the law-abiding, and that the statute is least restrictive means of accomplishing the policy end -- if all three of these prongs are not met, the statute will remain unconstitutional.
Now, under the current provision, a mere "reasonableness" standard -- easily met by showing a majority of legislature supported a statute -- is your only protection.
Let me know if I answered your question.
Okay! That's what we need to know.
The opposition wants EVERYONE to believe that as soon as this passes, someone is going to challenge ALL the gun laws they don't agree with; Concealed Permit Requirements, carry at college and school, churches, etc. This is their argument. It is hypothetical of course, but I've no doubt; someone is going to test some of them.
If we can make the public understand that this ISN'T a backdoor attempt (conspiracy), by the gun lobby (NRA and the like), to get this passed and go right after the existing laws, we can gain some points. I still believe we are losing the propaganda battle, but we'll see.
As noble an endeavor as I think we have here, I see where they (opposition), stand. My explanation to my legal eagles in the media was, if the Amendment passes, and the laws do get challenged, and do not pass muster (under strcit scrutiny), re-write the laws; and pass them again. There is never a shortage of new laws coming out of that place.
Unfortunately, the opposition doesn't want that either. Sooooooo.......