そして、どうすることも出来ない物憂さに、ふっとため息をつく。

、、。

And then, overcome by a helpless languor, you let out a quiet sigh.

Literal

And-then, do-anything-also cannot melancholy [to-に], softly sigh [object-を] let-out.

どうすることも出来ない 'unable to do anything about it' — total helplessness. 物憂さ 'languor, melancholy, listlessness.' ふっと 'softly, suddenly' — a gentle 擬態語. ため息をつく 'to heave a sigh.' Poetic and introspective — literary prose capturing a quiet moment of melancholy.