。
She was such a diligent girl that her French improved greatly.
Literal
She [topic-は] very diligent girl-was [because-ので] French [subject-が] greatly progressed.
勤勉 ('diligent, industrious') is a slightly bookish na-adjective, more at home in formal description than casual speech where 真面目 (earnest) might step in. 大いに ('greatly, immensely') is a literary adverb pairing with achievement verbs like 進歩する, 役立つ, 楽しむ. 進歩する is the Sino-Japanese verb for 'to progress, advance,' applied to skills, technology, society — anything that develops over time.