tough luck buddy, in that situation you can only explore Fountain Plaza after beating Julius, and you can check the hole where he came from if you want a rematch too.Trust me, the guy's not that hard just be prepared. Most of his attacks are predictable, eventually you just know how to dodge them, and just land a command or two on him, bring 2 healing spells with you, take hi-potions along if you want.
The commands i used to beat him with Riku were simple, really. Curaga,Cura,Hi-Potion,Shadowbreaker,Thunder dash, Prism Windmill,Blizzard Edge and Spark Dive. The commands i used with sora were similar, but i took out the Hi-potion and the Spark Dive for the Ars Arcanum, i just love that attack
Make sure to stock on Attack Boost if you wanna take out his hp faster, some Magic Haste to speed up the healing spells' cooldown and hp boost, cuz those are always good haha
Second chance and once more are a must.
That's about it, hope i helped ^^