A flange is a piece of fabric that is folded flat and inserted between the binding and the quilt top so that it sticks out a tiny bit. Its very easy to do and can add just the right bit of color to really bring a quilt to life!
French binding is binding that is a double thickness....vs. a single thickness of binding...For instance...when you cut your strip for binding 2 1/2 " wide, fold it in half longways...wrong sides together, then attach it to the quilt (you are sewing a double layer). Since you have 2 layers of fabric, it is more durable and is called a French binding...I dunno why.
Anyway...that is my understanding of both of these things. I have done a flange if you want to see a pic...I'll take one and post.