I live in Louisiana, and was wondering what the law is when your ex husband doesn't make contact with our kids in over a year mean? Does he still have the right to call after a year to make arrangements to pick up the kids or does he have NO rights what so ever?

A parent cannot be forced to be a parent. That does not mean they lost their rights. Only a court can terminate parental rights and courts are very reluctant to do so.

So the short answer is, no, he doesn't lose any rights.
The long answer is that, if he has court ordered visitation, then he can exercise those rights. But the custodial parent also has rights and can go to court to change or limit the visitation granted. If there isn't any court order, then either parent can go to court to set a visitation schedule. The lack of contact for an extended period will probably be considered by the court in whatever ruling they make.