Okay, this seems to be something different than the free ESO Plus weekend I thought it was. My bad.
There is a free trial of ESO+ running now, until Thursday 19th and that does include access to DLC (everything except Gold Road). But it doesn't start automatically, you don't get the benefits until you choose to activate it. You need to log into the game, open the Crown Store, go to the ESO+ tab and click the 'Free Trial' button at the bottom of the menu.
Once you've done that all your characters should have access to all the zones and dungeons except West Weald.
PC EU player | She/her/hers | PAWS (Positively Against Wrip-off Stuff) - Say No to Crown Crates!
"Remember in this game we call life that no one said it's fair"