This is essentially two questions.
Was the "race" of Romans anything like the people in Italy today?
Did the Romans speak Latin with "Italian accents"?
I'm curious because I want to know how to accurately depict Ancient Romans.
"Race" wasn't a thing until the modern period, at all. Romans talked, for instance, about Germans being taller and such, but they didn't have categories for people in that way (which may be a loss for us). How they talked, I don't know if we can recover. Some people think plays were done with certain gesticulations because not everyone could hear the words, but I think these theories draw on pictures of actors rather than written reports. I know Dutsch at UCSB has worked on this stuff, but I'm not sure I buy any of it. I would say we have no real idea of how Latin would be expressed in antiquity.
EDIT: Why was I downvoted in a matter of seconds? If I have the wrong idea, it's better to tell me where I screwed up rather than just bury me.
In their writings you can glean Martial was rather proud of his «stiff» Spanish hair and he was mocking the «blonde» barbarian slaves who acted like they owned everything in Rome. Cicero was mocking the Greek Chrysogonus in his Pro Roscio for his long «blond» hair as well.
In the 6th century BC Etruscan «tomb of the lionesses» you can see that even before Roman expansion light-haired people were around but not in the majority. The upper class also was already cosmopolitan.
source: A Companion to the Ethnicity in the Ancient Mediterranean by Jeremy McInterney
As to language, every Romance language is conservative in a different way. For the Old Florentine dialect ("Italian") it's the vowel length. In general Sardinian is regarded as the most conservative one still spoken but that's not something you can measure so easily. What's certain is Sardinian developed in a very different way from both the Western (Castilian, French, Occitan, Ligurian, Venetian etc.) and the Eastern (Florentine, Romanian, Napolitan, Sicilian etc.) Romance language dialects.
edit: just look at the murals from Pompeii to get a good idea how Romans looked in the first century CE.