。
She's qualified to teach both English and French.
Literal
She [topic-は] English [and-と] French [genitive-の] both [object-を] teach qualification [subject-が] exists.
両方 ('both') makes the inclusiveness explicit, removing any 'or' ambiguity from ~と~. The ~の両方 frame is the standard way to mean 'both of these': 男女の両方 ('both men and women'), 兄弟の両方 ('both brothers'). 資格がある ('have qualifications') and 資格を持っている ('hold qualifications') are paired counterparts — the existence frame focuses on the bare fact, the active possession frame on the holder. The relative clause 英語とフランス語の両方を教える modifies 資格 directly, packaging the entire scope of qualification ('teaching both English and French') into a single attribute.