They spoke a Tyrsenian language. The Tyrsenian languages include Etruscan of modern Italy, Lemnian of modern Greece and Raetic of modern Switzerland. All these langauges are dead, leaving only a bunch of inscriptions on graves and other short pieces of writing. They wrote with the Phonecian alphabet they learned from the Greeks.
There isn’t enough text to decipher the language or even relate the Tyrsenian languages to any other known languages. From studies of Indo-European the broad story of the languages of Europe was that Basque, Uralic and Kartvelian hunter and gathers lived throughout Europe. A wave of Afroasiatic speakers migrated in to form the first farming society, the Old Europe culture. Both the hunter and gathers’ and farmers’ societies disappeared as the horse-riding Indo-Europeans spread their pastoral culture and language from the Ukraine as far west as Ireland and and far east as the China. The Basques, Uralic Tribes and Kartvelians tribes shrunk and continued to survive as distinct cultures in pockets and on the periphery. The Afroasiatic languages and Old European society appears to have entirely disappeared.
So where must the Etruscans have fit into this? Already there were IE Celts to the north, IE Greeks to the eat and IE italic tribes on the way. It seems to me the odds of them being somehow related to the IE culture seems high.
It’s also possible that they are an isolate, which would mean they arrived really early, say 50,000 years ago, long enough for any relationship betwixt their language and others to have been washed out five times over. That, I fear is a question for the geneticists and the archeologist to decide.
And this amateur linguist is off to bed. Good night.