That sounds pretty good actually! The more focused your stats are, the better you are.
On a strength build, I would recommend you pick a weapon which moveset you really like, and upgrade it to the Crushing path (using Greystone). If you lack the materials you can always just bring it to +10, that should be decent too. If you like the longsword moveset, upgrade the Knight Sword instead (you should have picked it up shortly before the False King), it's the same thing except stronger and with better reach.
If you have enough intelligence (18), get the Curse Weapon spell from Yuria the Witch and use it to make your weapon very, very strong. It will drain your HP while it's active, but it's manageable. Better yet, if you use the Talisman of Beasts and
don't meet the requirements to use it (18 faith/magic), casting Curse Weapon with it will make the HP drain negligible. Not sure why, maybe not an intentional effect but oh well...
If you don't have enough int, use Warding, perhaps, though the False King's sword attacks are partially magical so it might not help that much. You can buff your weapon with turpentine or sticky white stuff instead, though I'm not sure how good that is against him.
Oh yeah, since his attacks are magic, you can perhaps block them with the Dark Silver Shield, though it might drain your stamina fast so it's better to roll.
Make sure you are always under 50% of your equip burden for the lighter roll. Heavy armour will not help you in this game, not ever. Stay mobile.
Good luck.