No, it is called ```Freedom of movement for workers in the European Union```.

https://en.wikipedia.org/wiki/Freedom_of_movement_for_worker...

That allows Europeans to migrate to other EU countries to work without requiring visas. It doesn't give them free entry into tourist attractions.

I believe this wouldn't matter. The right to charge toll is well-established, this has always included docking fees, and Venice is an island.

They can also regulate the amount of traffic, that's included in the sovereign rights associated with docks.

This means they can both charge entry, and limit access in a given day. I expect flatly refusing entry to specific people would be a different story.