What type of conditions existed in Europe prior to Charlemagne gaining power?
It is probably not entirely correct to say that the Roman Empire was "long gone." Remnants of old Roman cities remained, such as London, Paris, and Rome, although they were smaller and less significant than before. A number of Germanic Kingdoms, developed,including the Visigoths in Spain, who retained Roman customs and titles until Islamic forces destroyed their empire in 700 A.D. The Ostrogoths controlled much of Italy until it was reconquered by the Byzantine Emperor Justinian. Later, the Lombards invaded this area; however they were defeated by Pepin the Short who responded to a request from Pope Stephen II, who crossed the Alps to request Pepin's help. Pepin did not keep the territory which he conquered as his own; but rather gave it to the Pope as his personal fief. These lands became known as the Papal States and remained so for almost a thousand years.
The Germanic Tribes who succeeded the Roman Empire adopted many of its customs and traditions; including the embrace of Christianity. The most important person here is Clovis, who adopted Roman Christianity as a result of the influence of his wife Clotilda. By so doing, Clovis received the support of the Christian people of Europe, including the Pope, and was thus able to make the Franks the most powerful of the successor states to the old Empire.
Among the more important events of this time period is the Battle of Tours in which Charles Martel, the father of Pepin the Short defeated a Muslim army. His success stopped the spread of Islam into Europe and ensured that the continent would remain Christian. In fact it was soon thereafter known as Christendom for many years.
By the time just before Charlemagne took power in the late 700s, the Roman Empire was long gone. Europe was less unified politically and less connected economically than it had been.
By the mid-700s, the dominant power in Western Europe was the Merovingian Dynasty which had been created some 200 years before by Clovis. However, the Merovingians were not one united dynasty. Instead, there were various small states ruled by Merovingians. Just before Charlemagne, there was a move towards consolidation of these states by Charles Martel. However, this had not yet been accomplished.
Economically, there was much less trade than there had once been. There was still a great deal of trade by sea, but not nearly as much land trade as there had been in Roman times. This meant that the Frankish kingdoms ruled by the Merovingians were based almost solely on agriculture.