。
She looks happy.
Literal
She [topic-は] happy-seemingly is-visible.
幸福そうに見える pairs the visual evidential ~そう (used adverbially with に) with the perception verb 見える ('look, appear'). This double-marking — 'in a happy-looking way it appears' — is a stock pattern for describing impressions. Compare 幸福に見える (without そう), which feels slightly stiffer but works similarly. The そう adds a touch of inferred quality: the speaker is judging from outward signs.