woven horsehair, Horses tails and manes would have been used.
Althoug in the 1600's you had cotton and silk.
The best fishing line would obviously have been made from braided silk.
Silken thread and cord has been around europe since the middle ages.
If you can find a copy of izaak waltons - the compleate angler it will undoubtably tell you in there.
Try project guttenberg - as it's about 400 years out of copyright
http://www.gutenberg.org/etext/9198I'm going with hair and silk.