Background
The fall of Constantinople in the cold March of 618 did not mean the immediate end of the Eastern Roman Empire, but it certainly meant the beginning of a new era in Europe and the Mediterranean area.
The Sassanians had won the long war against Byzantium and their troops occupied Syria, Egypt and Anatolia. However,
Khosrau II, the Persian Emperor, did not want to extend the war further into the heart of the Balkans and preferred to let their Slavic and Avar allies to take the control of the Bosphorus under the Persian overlordship.
Despite the magnificent victory, Khosrau II never accomplished one of his most important wishes: the capture of the Roman Emperor,
Heraclius. The last Roman Emperor just vanished in the huge chaos which followed to the Byzantine evacuation of Contantinople: some people claimed he had died after the fall of the city, others said he had managed to fled the city...the only known fact is that the Sassanians never reached him, dead or alive. His fate after the fall of Constantinople has been a great mystery and the source of many unconfirmed theories.
Battle between Eastern Romans and Sassanian Persians in Constantinople.
But the disappearance of Heraclius was not just another mystery for the History. It became a huge problem for the surviving Roman Empire. After him, there was not an apparent heir to the Byzantine throne considering that Persians had captured, imprisoned or killed all his surviving relatives. This situation led to the bicephalia of the Empire: the troops in Greece proclaimed Emperor a general called
Theodossius while the elites which had sought refuge in Sicily proclaimed Emperor a local nobleman called
Iustus. But none of these claims received a wide popular support and neither the Pope (now, the only Patriarch not subdued to Ctesiphon) nor the Persians or other nations recognized them as legitimate successors of Heraclius.
The lack of a recognized head led to the fragmentation of the remaining Roman territories, specially between Greece (ruled by Theodossius) and the Italian/African territories (ruled by Iustus). Moreover. the Patriarchy of Constantinople, as well as the other Eastern Patriarchies, officially adopted the Nestorian Christianity, promoted by Ctesiphon, in 622; this change was not accepted by the Greek Church, so the local clergy created an alternate Patriarchy in Athens without consulting the Pope, claiming that this Patriarchy was just the relocation of the former Nicene Patriarchy in Constantinople. Even if
Pope Boniface V finally accepted the change, this fact started a tense rivalry between Rome and Athens, which increased the political distance between the both sides of the remaining Empire and thus, it made very difficult to achieve a compromise about the vacancy in the Imperial throne.
Anyway, the division of the Imperial remainders was not the biggest consequence of the fall of Contantinople. The boost in the settlement of Slavs and Avars in the Southeastern Balkans, Constantinople and some areas in Anatolia produced, once again, a major chain of demographic relocations in Central and Eastern Europe: the migration of Slavs and Avars southwards allowed other ethnic groups to fill (or re-fill) the depopulated areas. One good example were the Gepids: subdued by the Avars some decades before, the departure of many of them to the southern banks of the Danube allowed the Gepids to recreate the Second Gepid Kingdom in OTL Transylvania.
Finally, the most important change for the upcoming future was, with no doubt, the migration of many wendish tribes from the Oder valley to the south. The Saxons, allied with other German tribes like the Rugians or the Thuringians, would start a fast advance into these former wendish regions, subdueing the remaining ones and building up a strong confederation of tribes which will pose a serious threat for the Merovingian Franks.