Labelling requirements for selling cosmetics in Europe

Good afternoon. We are a Ltd company registered in the UK and selling only in the UK for the moment. We would like to make the product available across the EU as well. All our products comply with the EU cosmetic Directive, but we are unsure about labelling. Would anyone know if, selling though Amazon, the insertion of a multi-lingual leaflet in the Amazon shipping box would meet the EU labelling requirements?

Thank you.

Vittorio