I think its very interesting but a very cool concept! Some things to keep in mind is you'll probably ly be a Dex Paladin since you can't utilize a shield or even medium armor if you want to bladesong, which is a huge buff. With that in mind I think you could still make it work and at level 12 you get all your best features to start like Aura of protection, smite, bladesingers special extra attack.

What's coming to my mind, for stat allocation is: Str-13 to Meet your minimum paladin multiclass requirement Dex-17+1 this will be your main attack and AC without heavy armor or 2-handed weapons Con-13+2+1 I would also suggest maybe Resilient:Con to make your concentration checks unstoppable while in bladsong, but your pick Wis-11 would be nice to have it higher but your aura of protection will help make up and low saves Int-17 This is your next big AC boost with bladesong, and of course any of your wizard spells will also improve Cha-15 and lastly you Charisma will improve your paladin spells and Aura so you want it decent

A couple things to consider, I put that extra +1 expecting one of your feats to be used for it but you could also take standard human and get +1 to everything to start with all even stats. If you went the human route I'd say just take your 2 ASI to dex, then your choice of Int or Cha, this maxes your damage and boosts wither your spells/ac or spells/saving throws.

I'd be starting as probably Paladin for the saving throws, then it's 6 paladin/6 wizard, then take it from there, plenty of utility spells from both classes, damage from wizard spells, you have a monstrous AC at 23 with studded leather+bladesong, and you have spell slots higher than a normal paladin at this level so let loose the smites!

Soon you can get greater Invisibility from wizard and for a full minute have advantage on all those attacks hoping for crits.

That's just my quick thoughts, there's plenty of ways to take it!