Fear is a cool spell. It hits a good sized cone, is non-lethal, and can practically end a fight with a single casting.
However, since most enemies will closed to melee range as fast as possible and there's no way to exclude targets barring metamagic there's a risk of friendly fire if you can't get it off first. Of course the best time to cast it is when your enemies have grouped up to gang up on your poor fighter, when they're in a nice blob. However, you don't really want to scare fighter off too, do you?
The answer is simple: Countersong!
A Bard can play Countersong during their first turn, which then lasts till the end of their next turn. If during their next turn they cast fear, their friends will have advantage on the save and friendly fire will be less of a hazard.
Of course, if another bard or a paladin can drop heroism on the front line that's even better, but it's not something you can rely on. (Heroism and Fear are both concentration, so you can't use one to protect from the other on your lonesome 
. Of course if you can rope the wizard into casting fear...)
Aura of courage, unfortunately and inexcusably imho comes very late in the game - lvl 10, by which time fear will not be such an effective spell as in earlier game. Countersong seems like the best way to go about it, that is indeed a nice little tip. Maybe timing it with the fighter retreating after spending his action disengaging and moving out of the area of effect wouldnt be a bad way to go about it either, especially if the fighter uses a one-handed weapon (hence less damage on a successful hit). It will be essentially up to him, whether he wants to risk being affected (considering he rolls with advantage) or sacrificing one of his turns to disengage. And considering his build (weapon of choice, attack bonus and average damage, as well as saves, it can be calculated if it is better for him to risk it or just disengage).
Good idea, thanks for pointing it out.
You can use countercharm (action) and give your ally a bardic inspiration die (bonus action) on the same turn, in fact. You know, if he needs extra reassurance.
Keep calm emotions on hand, just in case.
Well, it should at least make countersong a bit more useful.
This same trick also works with Hypnotic Pattern btw.