Can one disinherit their children in Louisiana?

Sure. It's best to explicitly state in your will that you are leaving them nothing.
From:
Inheritance Rights

Generally, children have no right to inherit anything from their parents. In certain limited circumstances, however, children may be entitled to claim a share of a deceased parent's property. For example, the Florida constitution prohibits the head of a family from leaving his or her residence to anyone other than a spouse or minor child if either is alive.

Most states do have laws to protect against accidental disinheritance. These laws usually kick in if a child is born after the parent made a will that leaves property to siblings, and the parent never revises the will to include that child. The law presumes that the parent didn't intend to freeze out the newest child, but just didn't get around to revising the will. In that situation, the overlooked child may have a right to a significant part of the parent's assets.

In some states, these laws apply not only to children, but also to any grandchildren of a child who has died.

If you decide to disinherit a child, or the child of a deceased child, your will should clearly state your intention. And if you have a new child after you've made your will, remember to make a new will.