She speaks French fluently, not to mention English.

Literal

She [topic-は] English [topic-は] needless-to-say, French [also-も] fluently can-speak.

The ~は言うまでもなく frame topicalizes English as obvious and adds French as the new fact. 流暢 is a Sino-Japanese な-adjective ('fluent / flowing'), almost exclusively reached for in the language-skill context — its kanji 流 ('flow') + 暢 ('expand, flowing freely') paint speech as something that pours out smoothly. The adverbial form 流暢に modifies 話せる (the simple potential of 話す). Outside formal discussions of language, native speakers tend to use the everyday alternative ペラペラ, a colloquial mimetic for 'speaking fluently.'