The Romans spoke Latin, but it wasn’t the Classical Latin language that it taught in schools and universities today. The Romans would have spoken Vulgar Latin, and used Classical Latin for their writing and official events and ceremonies. Vulgar Latin was not standard and is sometimes known as Common Latin or Colloquial Latin.
The Romance Languages (such as Spanish, French, Portuguese, Romanian and Italian) all evolved from the same starting point following the fall of the Western Roman Empire – Vulgar Latin. Over time they developed into completely separate languages.
In the Eastern Roman Empire, based around Constantinople, by the 4th century, the official language was Greek and not Latin.
Click this link to learn more about the Romans.