Not only does she speak English, she speaks French fluently too.

Literal

She [topic-は] English [only-だけ] [is-not-でなく] French [also-も] fluently speaks.

The ~だけでなく~も pattern packages two languages together with French upgraded by the adverb 流暢に ('fluently'). The pairing of the construction with 流暢に raises the stakes: it's not just 'also speaks French' but 'also speaks French at a fluent level.' Note the rhythm — by topicalizing English (already known) and then introducing French as the more impressive case, the sentence builds emphasis through information staging rather than emphatic words alone. This is typical of how Japanese encodes emphasis structurally rather than with stress or volume.