Yes, you need to apply for the free Priority Pass. This is a good deal and one of the best perks of Plat Amex. See PriorityPass.com for more details. You will get a separate card that you need to show for entry.

The only exception - for UK members, at least - is the lounge at the Eurostar train terminals in Paris and London, and the BMI and (I think) Continental airlines lounges in the UK. You get into these simply by showing your Plat card.