。
She was born in a small village.
Literal
She [topic-は] small village [at-で] was-born.
~で生まれる ('to be born in [place]') uses で in its location-of-action sense. 小さな is one of the irregular pre-nominal adjectives: it can only modify a noun directly, never serve as a predicate. Compare 小さい (the regular い-adjective) — 村は小さい ('the village is small') is fine, but 村は小さな would be wrong. The polite ~ました ending suggests a biographical context: a self-introduction, an interview, or the opening line of a memoir.