What language is Latin based off of?

Latin is not based off of any other language. It is considered a proto-Indo-European language, which means it's an ancestor to many other languages but doesn't have a direct ancestor itself.

While scholars have reconstructed a hypothetical proto-Indo-European language, it was never written and is only theorized. Latin is considered one of the earliest attested Indo-European languages, with its earliest written records dating back to the 7th century BC.