The future progressive tense is used when expressing events and action in progress at some future point, however the example sentence cannot be understood in that way.
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 I breathe a sigh from melancholy in being unable to do anything about it.
なによ!出来ないの?この度胸なし!腰抜けッ!
What? You can't do it? You coward! Chicken!
蓮くんは察しは良い様だけど、もう少し心の機微というものを理解出来る様に努力するべきじゃないかしら。
You're considerate, but don't you think you should work a little more at understanding the subtleties of the human mind?