。
She sang as if she were enjoying herself.
Literal
She [topic-は] enjoying-seemingly sang.
楽しそうに combines 楽しい ('fun, enjoyable') + そう (the visible-evidence そう attached to adjectives, dropping the final い) + に (adverbial form). The result is 'in a manner that looks like she was having fun.' Note that そう attached to adjectives means 'looks/seems X' from external evidence — distinct from そう attached to plain-form predicates, which means 'I hear that X' (hearsay). The に turns the whole thing into an adverb modifying 歌った ('sang'). 楽しそうに歌う is the everyday phrase for singing happily — singing in a way that *displays* enjoyment, observable from outside. Whether she was actually enjoying it is left open: そう reports appearance, not certified inner state.