My opinion - If you want to just tinker on the bike, replace the front derailleur/shifter/cable to get that front shifting working good-as or better-than new.
The spring on my Tourney front derailleur is currently weak and I can only get two gears out of it - left and center, or center and right. I have it set up for center and right, and for the 2% when I need it left, I can "throw" it into gear without stopping by shifting both shifters to the left simultaneously.
I have vacation this week, so maybe I'll get around to fixing it.