Literally, when the word “debut” was two words in French, de but, it meant “from the mark.”
It was used just as we say, “your first stroke,” in billiards, “your lead,” in cards, or “your first throw,” in dice.
In other words, it signified the opening move or play in a game. From that expression, a French verb was coined, debuter, to lead off in a game.
This meaning was then extended into to make one’s first appearance (upon the stage, into society, or the like).
The French verb and the noun created from it, debut, retain the original and the extended senses, but we borrowed the noun only, now Anglicized to debut, and retained only the extended senses.