Thank you for your question. I look forward to working with you to provide you the information you are seeking for educational purposes only.
Does your parish have any ordinances regarding assemblies, for example I know Jefferson and Orleans and St. Tammany have ordinances requiring those who are seeking to protest to obtain permits from the police?
Under the LA laws, disturbing the peace (RS 14:103) would be the law most commonly used if the protest interferes with the operation with the school. The protesters also cannot block the sidewalks or interfere in any way with people entering or exiting the school property. However, they can assemble on PUBLIC property, not school property, and they are allowed to protest, as that is their 1st Amendment constitutional right.
There is also LA RS 14:40.6, which prevents anyone from interfering with operations of the school. Lawful and peaceful protest off school property, even in view of the school, that does not interfere with anyone entering or leaving the school or cause traffic problems with parents getting students to school would not be a violation of this statute. If they do interfere in any way with the actual operation of the school, then they could be arrested for this charge in addition to the 14:103.
So, legally, you as a sheriff's office have a right to set up rules and a protest area outside of the school property and restrict protesters to that area, or you can simply inform the protesters that if they stay off school property, do not interfere with anyone entering or leaving the school and do not cause traffic problems for those getting to the school, they have a constitutional right to engage in lawful protest (and if your Parish has a permit process you can make them apply for a permit for the assembly and pay for a police detail as well if the parish ordinance provides for that).