I'm currently setting up a backstory for my elf bard, and I wanted her father to be out of the picture due to some type of enslavement or maybe a contract with the fey. He actually was a good father so I'm struggling to come up with an in character reason he would make a deal/contract with fey. My bards mother is currently falsely imprisoned so I thought maybe that could be a motivation. Any ideas?

If he's a good person, the Fey could have appealed to his kinder side, e.g. by pretending to need help and telling him it needs a fruit from that coincidentally nearby tree which happens to be its sacred tree and as punishment he's enslaved or forced into a contract or something

desperation works great too - having exhausted the worldly options to free his wife, he tried the otherworldly, but he was too trusting for his own good and got tricked.

Debts of some kind are always a great way to force people into contracts they wouldn't normally consider.

accident - like the woodcutter cutting down the fairy's tree and getting cursed as a result.

(Here I am working under the assumption that it's a bad contract which seems to be what you're looking for, but it could be good):

maybe he did a fey a favour and now it owes him one

Hope this helps.

Thank you!

It seems that something similar to an Infernal Contract would work well. Maybe he stole an artifact or crossed an archfey. The other fey could have given him mercy, and instead of an execution, maybe he has to complete some impossible task (perhaps taking inspiration from Grimm's fairy tales) or a favor to free your character's mother. Possibly if you work it out with your DM, it could become a plot hook, or help you flesh out their backstory further. 

Maybe your character was sick, and he cut a deal with the fey to heal you. I can see lots of interesting opportunities in either you knowing what he did, or not knowing.