Who SPOKE Classical Latin in Rome?

I wander could someone suppose that social groups or people in Ancient Rome
actually used Classical Latin, not Vulgar one, i.e. spoke it in theirs usual
everyday life, for everyday communication? Poets, orators, high classes?..
Who else?

You see, I'd like to make them the ancestors of my Romula conlang speakers,
to explain why Romula is so close to Classical (not Vulgar) Latin in
vocabulary, so archaic.

Artyom.
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