This is quite a complicated issue, and I'm not expert on it, but I'll try to explain it the best way I can.

To be honest, it were the Romans themselves who caused their own downfall. After the dead of Marcus Aurelius and Commodus (the guy from the Gladiator) many powerful Roman figures tried to acquire emperorship. Big problem: Legions were more loyal to their generals (who payed them) than to the Roman state. Therefore aspiring generals used their legions to fight those of a rival. This happened many times during the 3rd and 4th century AD. While the first two centuries after the birth of Christ were relatively peaceful (Pax Romana), the two centuries that followed weren't. No generation could grow up without witnessing a civil war.

Normally, most of the legions were stationed at the borders, to protect the empire from incursions by barbarian plunderers. But now many legions were pulled away to fight one of their generals' rivals. This left the borders relatively defenseless. This lead to more and more raiding parties coming in from over the Rhine. Note: we're talking of groups of bandits here, not real armies who seek to conquer. The Germanic tribes were not unified and there never was such thing as a "Germanic" or "Barbarian" army. Mainly just bands of warriors who followed a chief. If the chief died, they would look for employment elsewhere.

While the Romans were fighting their civil wars, they realized they needed to do something to protect the borders. So they called in Germanic warlords from over the Rhine to settle in border regions. They would acquire some form of autonomy in exchange for keeping other barbarians out. Those barbarians were called 'foederati'. The Germans were happy to settle, because they could freely trade within the Roman Empire (which basically was a gigantic, integrated economic zone), the Roman Empire was more politically stable than their homeland (which saw a lot of warfare beween rivalling warlords) and because of the pressure of the Huns.

The emperors and their rivals quickly saw the potential of these new warriors and started to recruit them into their armies, which allowed some barbarians to rise to the top of Roman society. Forget the barbarians you see on tv. These guys were as well dressed and behaved as ordinary Romans. They simply had a different ancestry.

So now German dudes were starting to have armies within Rome. De jure under Roman controll, but as I said earlier, it mostly were the generals themselves who payed their legions and so he soldiers were loyal to their general instead of the state. When the Visigoths under Alaric sacked Rome in 410, it is wrong to think of Alaric as a vicious barbarian leading a barbaric horde. Alaric was in fact sent by the Eastern Roman Emperor (I forgot who it was at the time, but that doesn't really matter) as a (Roman) general to fight one of the emperors rivals there. Alarics army probably didn't exist solely of Visigoths, but probably counted many other barbarians and even people native to the Roman empire (Greeks, Thracians,...). But since Alaric himself was a (Romanized) Visigoth, it is often said that the Visigoths sacked Rome.

Anyhow, state authority in the West was declining because of the political chaos. Which gave many local military leaders the chance to fill the power gap. Many of those leaders were of Germanic descent, but there were also Romans, like Syagrius, who established a tiny kingdom in Gaul that was eventually eaten by the Frankish Kingdom of Childeric and Clovis. (The Germans were often a Roman General and King of their own tribe.) The newcomers often married into the local elite to inherit local wealth and possessions.

When Romulus Augustulus was deposed by Odoacer, Odoacer did not mean to end the (Western) Roman Empire. In fact, he sent the jewels that resembled imperial authority to the Eastern Roman Empire, who was seen as the new Western Empire. Odoacer basically wanted to reunite the Empire. So the Roman Empire did not end de jure in the West, but it did de facto. All the various kings of the kingdoms that were established in the West would 'swear allegiance' to the Emperor in Constantinople. Though, in practice the emperor had nothing to say. And thus the empire had ceased to exist in the West.

In latere stages (8th century), the Franks would eventually rise to be the most dominant power. They would conquer all of modern day France, Belgium, Netherlands, Luxemburg, most of Germany and some parts of Spain under Charlemagne. It was costum among the Germanic peoples that when a father died, his belongings would be split among his sons. So when Charlemagne's sole surviving son, Louis the Pious, died, the Frankish empire would be divided among Louis' sons. Charles the Bald got West Francia, Louis the German would get East Francia and Lotharius would get Middle Francia. Lotharius died soon after, and again his realm was divided among his sons. Those died as well and all of Middle Francia was incorporated in either West- or East-Francia. West Francia would later become France. East Francia would become the Holy Roman Empire and later Germany.

I hope this helped.