。
She studied French as hard as she could.
Literal
She [topic-は] as-much-as-possible wholeheartedly French [object-を] studied.
できるだけ (as much as possible) and 一生懸命 (with all one's might) stack for emphasis on maximum effort — できるだけ sets the upper bound while 一生懸命 describes the intensity within that bound. フランス語 uses the pattern [country name] + 語 to form language names — フランス (France) + 語 (language). 一生懸命, literally 'one life, at risk,' originally referred to a samurai's commitment to defending one estate (一所懸命) before evolving into the general expression for giving something your all.