She can't speak English — let alone French, that's out of the question.

Literal

She [topic-は] English [object-を] cannot-speak, much less French [such as-なんて] outrageous is.

ましてや is an emphatic version of まして ('even more so / let alone'), used when escalating from one negative claim to a more extreme one — 'if she can't even do X, then Y is right out.' The follow-up clause uses ~なんて to dismiss the possibility of French scornfully and もってのほか ('outrageous, out of the question') to slam the door. もってのほか is itself a fossil idiom: literally 'beyond holding,' i.e. beyond consideration — written in old kanji as 以ての外, but the kana spelling is far more common. The combined effect is sharply emphatic, almost theatrical.