Fiat paper currency and fractional reserve are basically independent concepts. Fractional reserve is practiced by the banks, and was done under gold-backed currency just as much as today. A really interesting thing is the period of "Free Banking"[0] -- in Scotland in the 1700s/1800s where banks were essentially unregulated; State banks in the US were loosely regulated in much of the 1800s as well.
All that's required to do fractional reserve is the ability to distinguish "money on account" from notes. Either issue private notes, or maintain ledgers of balances.
You could conceivably have a 100% reserved bank (doing bailment of physical fiat notes -- a $100 note in the vault for every $100 in a savings account balance) even under fiat currency. Or you could have something with only one entity allowed to increase the money supply (deposit with the central bank, but a 100% central bank reserve requirement, but the central bank allowed to do loans).