you would never say in english 'as you can notice' you would say 'as you can see'.
"As you can notice" works here. Although yours is probably used more often, I won't say the given translation is outrageous by any means.
"As you can notice" sounds very odd - not saying it's incorrect, but we usually say "as you might have noticed" or "you will notice" but "as you can see," as rosmcculloch said.
Does anyone know why the word 'le' is used in the French sentence?
I think it's because it refers to the other person (to whom you have a very different character) I assume. :-)