In French, it gave "charme"!
Because "carmen" was a poem/or a song/or an ode/or a religious formula.
This last meaning was kept in the word "charme".
This word became: a magical incantation (only this meaning in old French), and later became synonym of someone who is so pretty or attractive, or whatever, that this person seems to use a "charme", so they started to say that this person had a "charme". (= a mysterious thing that makes them attractive, we don't know how)
And later, this word was borrowed in English, in charming (charmant), and charm. to charm (charmer).
In modern French, the meaning "likeability" is now the more common, but the word has still this meaning of "sort, incantation".
Okay, thanks, I'll keep my eyes open.
About the notation, just by curiosity: from Tolkien, I am used to be given the stem in a dictionary in the pattern "Carmen (Carmin-)" Why do the Latin dictionaries note it like "Carmen, Carminis"? Now, I understand Carminis is the genitive and we know the genitive suffix if we know gender and declension type and thus we can deduce the stem, but why make it so complicated? If they want to tell us the stem, then why don't they just tell us the stem and nothing else attached?