Can I share Paramount+ on my Smart TV without Apple TV?

if your smart tv support airplay 2 then you can unless paramount+ block airplay as it strip their media from the DRM that copy protect it

if they do you need to buy the appletv box and install the paramount app on it

If you subscribed via Apple you need the Apple TV box to watch through the Apple TV App. If you subscribed through paramount you can install the paramount App on your smart tv and sign in with the email and password you’re using for it. See: https://help.paramountplus.com/s/article/PD-I-m-an-existing-subscriber-How-can-I-watch-Paramount-on-my-connected-device