Since asking this question I managed to beat him. This is how I did it:
- Left Hand: Purple Flame Shield +9, Talisman of Beasts
- Right Hand: Crescent Falchion +4, Sticky Compound Short Bow +5 (normal arrows)
- Magic: Warding
I think any decent sword/shield combo would work, as would a Catalyst instead of the Talisman. Any bow would be fine.
- Have the shield and sword combination selected most of the time.
- Be prepared to quickly switch to bow and fire off a shot (or use a throwing weapon)
- Cast Warding before engaging. Recast when the opportunity arises.
- Have healing items in your quick-access slot. Heal when the opportunity arise.
- Be patient and don't push your luck with too many successive hits.
- Keep your stamina up by lowering your sheild when possible.
- Stay away from him whenever possible.
I've found the opportunity for healing/recasting of Warding to be just after the False King has performed his final successive shockwave move, as long as you are not within sword-striking range.
The False King has a few different types of attacks:
- AoE explosion spell
- Charge and swipe
- Multiple swipe with shockwave
- Soulsucker (steals one of your Soul Levels)
AoE explosion spell
Don't try to outrun or block this. Instead switch to the bow and shoot him, interrupting the spell. The spell charge time is long enough to allow this. A thrown weapon would probably work just as well.
Charge and swipe
Roll out of the way, turn and hit him 1 or 2 times, then back away. This is the only safe time to attack via sword.
Multiple swipe with shockwave
If you're close, block his hits with your shield and roll/move away as soon as possible.
If you're further away, move sideways to avoid the shockwave, or block it with your shield.
If his hand is glowing bright white, he is preparing the Soulsucker move. Roll away as fast as possible.
Keep this up and the False King will be yet another Demon's Soul in your cap.