Immigration work is federal, so your local edge is the reader and not the law
The statutes do not change at the parish line, but everything about how a client finds you and decides to trust you does.
Louisiana runs on a civil law tradition rather than the common law used in the other states. Family and property firms across Orleans Parish build entire marketing programs on that difference, and they are right to. Your work is federal, so the honest position is to note the distinction rather than claim it.
The difference still matters to you in one specific way. Legal content bought from a national vendor is written for a common law audience and for other states' court systems, and around here that shows. Readers notice. So do the local firms competing with you for the same referral relationships.
Localize the reader instead of the law. Where the office is and how long the drive takes, which languages your intake can actually answer in, what a consultation costs, who will be in the room, what a client should bring. None of it is federal, and all of it decides who calls.
Where a matter touches state court or state records, keep the page general and send people to their own counsel. Generally the safest structure is to describe the process your firm runs and stop short of advice.