The Early Middle Ages comes after the fall of Rome, about 400 AD. But all the way through the Early Middle Ages, European people still thought of themselves as living in the Roman Empire and being Romans. Even armies who had invaded by force thought they were Romans. Even armies who were fighting the Romans thought they were Romans. Being Roman was so popular that even people who had never been inside the old Roman Empire thought they were Romans.
To save money, the Roman emperors hired Germanic people to work as Roman soldiers. Gradually these Germanic soldiers moved into the Roman Empire and settled down to become Romans themselves. The Visigoths settled in Spain, the Vandals in North Africa, the Ostrogoths in Italy, and the Franks in France. In England, a commander we know as King Arthur tried to keep out the Angles and the Saxons and the Danes (the Vikings), but they, too, moved into the Roman Empire. Together, these invaders fought with Roman soldiers to push back the Huns in 451 AD.
In 533 AD, the Roman emperor Justinian tried to get rid of all these invaders and rebuild the Roman Empire the way it used to be. His armies recaptured North Africa from the Vandals, and Italy from the Ostrogoths, and some of Spain from the Visigoths, but then they stopped there, and the other Germanic invaders stayed inside the Empire. But the wars had weakened the Empire even more, and then in 542 AD the bubonic plague struck Constantinople and soon spread all over Europe and North Africa, killing thousands or millions of people. By 600 AD, the Lombards took advantage of this weakness to move into Italy, and the Slavs moved into Eastern Europe.
But even then, people still continued to try to rebuild the Roman Empire. In the 600s AD, Islamic armies reunited Jerusalem and Syria, North Africa and then, in 711, Spain. By 780, Charlemagne copied this idea in France and Germany, calling his kingdom the Holy Roman Empire. To the east, in Russia, the Vikings and Slavs got together to build a kingdom too. All of these thought they were rebuilding the Roman Empire.