。
She's qualified to teach English and French.
Literal
She [topic-は] English [and-と] French [object-を] teach qualification [object-を] is-holding.
資格を持つ ('to hold qualifications') is the active counterpart of 資格がある ('to have qualifications'); both are common, with 持つ feeling a touch more deliberate — qualifications acquired and currently held — while ~がある focuses on bare existence. The relative clause 英語とフランス語を教える ('teach English and French') sits before 資格, modifying it as 'qualifications-for-teaching-X-and-Y.' ~ている on 持つ marks ongoing possession, the same as 知っている for ongoing knowledge.