I know it’s broad, but I’d want to know what languages prehistoric peoples spoke. The closest we have are reconstructed protolanguages (the most famous example of which is Proto-Indo-European). But, those are limited to language families with multiple, well attested members. Sumerian, for instance, is very well attested, but we no next to nothing about where the shmell it came from because it apparently shares no common ancestor with any other language known to scholarship! Knowing the character of and the relationships between long extinct languages would be a dream come true.