Knowing that there’s alot of legal issues in the fanfic world, I’d feel better knowing they’re okay with it before I do it.
I’ve never seen Pixar take any major stance on copyright issues, outside of them removing the copies of Presto that showed up on YouTube (of course that could’ve been Disney’s lawyers). Disney, on the other hand, like to do the whole giant empire thing and I’m sure there could be issues there. However, if you don’t try to make money off of it or promote it as official, I doubt they’ll be able to do anything, even if they wanted to.
Welcome to Pixar Planet, Jimmy Vietnam! 
Well, I’m pretty sure Pixar doesn’t care if people make fan-fiction based on their characters just for fun. Just never send any of your original work to Pixar, because as you may know, they develop all of their stories in-house, and they never accept unsolicited outside work. Also never sell your Pixar stories, because that would be illegal. I don’t think you’re going to do any of the things I listed above, so you should be in the clear. 
First off, welcome to PIxar Planet.
And I’ll tell you that I write fanfiction myself. I was a little afraid about doing something illegal. BUt i think that if you are a fan of Pixar, then I am sure Pixar would want you to express that fandom to the world. What I do is give a little disclaimer before I post my first chapter.
If it’s just for fun and it’s casual, I’m sure they don’t mind. A disclaimer at the beginning of each chapter, just to make it clear that they’re not your characters, is a pretty good idea.
And welcome to the forums, Jimmy Vietnam!
Welcome, and hey! Aren’t you that guy that made “Hello, Wall-E!”?
A disclaimer should clear it up.
Yeah, I wrote Hello, WALL-E. It’s currently taken down, and is being revised. It will be up again soon, though. Don’t worry.
As long as you dont sell it and dont try to pass off the characters as your own (like TSS said, a disclaimer is the easiest way to avoid that, although I’m sure by now most people reading the story will know where the characters came from) you’ll be fine.