5 fighters and a barbarian is fine….maybe not for Curse of Strahd….but it is fine. I generally disagree with anyone who suggest any kind of forcing players to pick different characters. Let them play the character they want, if not you are already starting out on the wrong foot. DnD is extremely adaptable. I personally always let my players pick whatever they want without any knowledge of what the other PCs are going to be. It hasn’t quite put me in this precarious of a spot though. Honestly I think running a table for this party could be a lot of fun..... just not on CoS.   

My suggestion would be, let them all know that there are 5 fighters and a barbarian, let them know that is fine, but might not work for CoS. If the party is dead set on playing CoS, as 5 fighters and a barbarian let them. I would just dump more health potions/ magic items into the campaign.  If they are not dead set on CoS I would let them run with what they have picked and do a homebrew , I have not ran any of the predesigned modules suggested for this kind of party makeup so I can’t speak to them being good or not, there might be something out there you can get without homebrewing.     

Overall I think the biggest issue you will encounter with this is, as has been stated by others here, that there will not be a lot of shining moments for PCs that organically happen. It will require a lot more work on your part to make sure that everyone gets that opportunity to feel like their character mattered.

Quote from Sanvael >>

There's no reason that they'll die, but it will be a fairly dreary campaign since they have few options. With no Cleric or Paladin they cannot use the Symbol of Ravenkind, and will have a really limited set of abilities to deal with problems in interesting ways. Moreover, they'll find that most of them rarely get to feel special, since everyone else can do what they do.

I'd tell them that there are five Fighters in the party, and ask them whether any of them would like to change class. You may well find that several of them are happy to switch to another class. Mention to them that in order to have moments where they get to shine, it will probably be more fun if there is a range of classes. I think you'll find your players are happy to reevaluate their choices.

Alternatively, ask them to rate how much they want to play a fighter over any other class, on a scale of 1 to 5. On a 4 or 5 they keep playing Fighter. On a 2 or 3, ask them to consider changing. On a 1, tell them that you'd appreciate it if they changed class. If everyone chooses 4 or 5, then let them run an all-fighter party. If you think they're finding it a bit grey and some of them want to change mid-campaign, ramp up the difficulty of encounters to a near impossible level and let 2-3 of them die off early.

 One or more could multiclass, fighter paladin/fighter cleric can work well. 

Some fighters can use magic (EK subclass), and some fighter builds actually work as archers (dont underistamate +2 to ranged attacks from archery fighting style).

Your party could work depending on what other options (race, backround, soon subclass) your players take.