Paypal is not itself insured by FDIC, the banks they deal with are.
here is part of there statement on fdic:
FDIC pass-through deposit insurance protects you only against the failure of the bank at which PayPal places your funds, and does NOT protect you against PayPal's insolvency. Through the terms of our User Agreement, we believe that your funds will also be protected from any claims of PayPal's creditors and will be returned to you even in the unlikely event of a PayPal insolvency
Checking the FDIC database shown no listing for Paypal.
http://www3.fdic.gov/idasp/
Paypal is not a bank, lending institution, or a credit card company, there is really no law on how they deal with your money.