Here's the breakdown:
* Latin "salūs" -> Medieval Latin "salut" (meaning "health, safety, well-being") -> French "salut"
The original meaning of "salut" was a greeting wishing someone good health. Over time, it evolved into a general greeting, similar to "hello" or "goodbye" in English.
It's interesting to note that the Latin root "salūs" also gives us the English word "salvation," which relates to the idea of spiritual well-being.