She looks happy.

Literal

She [topic-は] happy-seemingly is-visible.

幸せそうに見える pairs the visual evidential ~そう (in adverbial form ~に) with the perception verb 見える ('look, appear') — 'in a happy-seeming way, appears.' The doubled marking is a stock pattern for impressions: そう adds the inference that the speaker is reading outward signs. Native 幸せ gives the sentence a warm, conversational feel; the Sino-Japanese 幸福 in the same frame would land slightly more formal.