The Falfurrias site says the name right.

Falfurrias is one of those Texas towns that looks nothing like it sounds. We put a note on the site that says 'Fal is how people actually say it.' Not the full formal name, just Fal. We answer the question before somebody has to ask.

Small details like that make a difference when you're trying to sound like you belong in a place instead of like you're reading a script.