First thing we do, when it comes to a website redesign is to analyse the current website. Carefully look through it and make a lot of annotations to help us find the key pain points & also get to the "Why" some things are there.
When something was unclear to us, we just asked Olivier and his team a couple of questions, since they are the experts in their own field. Why is there a form? Do we really need a graph in the main header? What problem are you trying to solve with the redesign?
All of this helps us to understand the client needs, what problem are we trying to solve & does this make sense for the target market?