I know this is my second post here but I've been doing historical reenactment for quite a while, specifically in regards to the 17th and 18th centuries. What Connor is wearing is a form of late justacorps (pirate coat to most people), tailcoat, or frock coat. It's highly stylized (it is a video game), where the 16th through the 18th centuries are present within the style of the coat. However, beyond the history of his coat, it is easy to replicate in a variety of ways.
One: the easy but most expensive route would be to buy a white trench coat and modify it. Note how I said it is the easiest (sort of) but also the most expensive. Good quality trench coats are expensive.
Two: my preferred way, would be to make a pattern for the coat and make it from scratch. It is rather daunting, but nothing a veteran 405th can't handle. Here's some resources to help you on your way:
http://www.sutlers.co.uk/acatalog/18thbrown.jpg
http://www.jpryan.com/images/g1750coat.gif
http://www.polyvore.com/cgi/img-thing?.out=jpg&size=l&tid=3497002
http://thecostumersmanifesto.com/costumeoldsite/history/leloir/justaucorpspattern.jpg
It's much the same as building armor for a Spartan when it comes to options. It really depends on the quality of coat you wish to have and the amount of time you wish to put into it. My girlfriend made for me from our own modified historical patterns a circa 1660's justacorps that was inspired by Hector Barbossa in POTC. This coat was an arduous project that took probably a total of 100 hours to complete. But the fabrics are period, the stitches are correct and it is tailor made custom to me. To me, this coat is priceless.
The important thing about it is the type of fabric chosen to look the part. Traditionally a worsted wool, jacquard, or velvet, in that order of poor to rich, would have been used for the coats in the late 18th century. I highly recommend you check out this book "Men's 17th & 18th century costume, cut & fashion: patterns for men's costumes" by Ronald I. Davis, and William-Alan Landes. I'm sure your local library could find a copy through their inter-library exchange as the book is rather expensive. I own a copy and for what I do it is worth every penny. Here's a link for the book on google:
https://www.google.com/shopping/pro...a=X&ei=Niy9UM-_IMnWiwKti4CwAQ&ved=0CGEQ8gIwBA
Also if you would like any help on designing the coat, feel free to PM me as I'm already working on this very coat myself. Connor is by far my favorite Assassin yet, and I've yet to play the game even. It's more the time period and location that does it for me, and I know Ubisoft did it right.
Fair winds, following seas
MSgt