Max demonstrated crosswind, from our books, is 38kts including gusts for both dry and wet runways.
Mr. ECAM, if you look under limitations in the manufacturer's certification data, there are published numbers for
continuous crosswind limits and that number for the A320 is 33 knots with dry runway/good braking. This is a certification number - many airlines publish their own, often lesser limits.
I was using a commonly accepted standard to describe the limits -
maximum continuous crosswind - which is also a
certification standard. For whatever reason, Airbus chooses to publish their own additional limits, including gusts, naturally raising the figures.
Since the numbers are demonstrated using Normal and Direct Law, it is not a FBW limitation. My earlier post,
here, includes the general design reasons for the limits if you are interested.