The name itself is also derived from the shah title, many languages use a still very similar name for it. For example, in German it is called Schach, and checkmate is Schach-Matt.
I am not a specialist of old french, but m'aider would mean "to help myself" in modern french
Interesting fact, in french the Checkmate etymology gave "Échec et mat", which litterally meants "Failure and beaten" and the game is called "Échec".