You can have the assessed value of your home frozen so that reassessments do not push it up. This freezes the assessed value only, not your tax bill, so what you owe can still change if the tax rate rises or you enlarge the living area.
Contact your local parish tax assessor to apply. This is a parish-level filing, not a state one.
Proof that you own the home and live in it, your income information, and your VA rating documentation, casualty documentation or marriage certificate depending on how you qualify.