Do Fulfillment agencies for the EU really exists?

One of my side businesses is an accessories/apparel dropshipping business, doing good enough but taking way too much of my time to do it correctly: import best sellers, deal with custom packaging, shipping, etc.

I'm playing with the idea of handing over the logistics to a fulfillment agency. Does anyone know a reliable fulfillment agency focused on the European market (France, Benelux) able to manage custom branded packaging, custom thank you notes and shipping (I need the packages delivered within 4-7days)?

So far, I didn't find anything who can offer that for the EU.