Per Byzantine sources the Franks were, as late as 550, a relatively minor Germanic Tribe living in Gaul. Yet within 300 years Frankish Tribes had basically set the foundation for every major Pre-Modern European Power (German City States, HRE, France, Spain, England).
So why were the Franks so successful in land power projection?
These people didn't come out of the wilderness, but from Roman-Iron age Germany. They were a powerful tribe which controlled the lower Rhine, (so were the Saxons). This period of Germany is called the Jastorf period and they traded with the Roman Empire and Scythians. Before they were dependable allies of the Roman Empire, they were pirating the coasts of Gaul and Britain along with Frisii and Saxons. They occupied Batavia which was an ideal location for their pirating. It was also adjacent to the most distant, penetrable Roman border. Saxons pushed them from this location into Gaul. Due to their location, they were the first tribe to successfully settle in the late Roman Empire, a trend which others would follow. This was not totally accidental, the best a Germanic ruler could hope for was to enter into the service of the Empire. This began their relationship with the Roman Empire. They were Foederati in Northern Gaul, and by the fall of the Roman Empire, a few were Magister Millitum. They moved to the lower Somme, with their capitol at Tournai, and this became the base of their expansion. It was ideally located, and they continued to have the ocean at their back as they grew. The Battle of Catulian Plains was pivotal for the Salian Franks. I haven't studied it much because of its enigma, but it seems to have determined the pecking order for Western Europe.
They were already a prestigious Germanic people, and to add to this, they were the only Barbarians in Gaul to convert to Catholicism. (A few other Alans may have been.) So they assumed the legacy of the Roman Empire, and then the new Roman faith. They had a string of victories in the name of Catholicism. Dagobert's daughter married Aethelbert of Kent, which initiated the conversion of the Anglo Saxons. Their success was under the Catholic auspices. When it came time to manage their kingdom, Merovingians could not. The church took advantage of this and moved into governance. They don't appear to have had their own realistic goals. They had a job to do, they did it, and that was it. They were great "Magister Militum" and nothing more. Whatever Charlemagne is credited for, he didn't create a lasting kingdom. The question is therefore, why did Catholicism prevail over Arianism? Arianism was the tool of the Byzantine court. It was because of the Huns, Lombards, and other impediments to the Eastern Empire before and after it reconquered Italy. With all these setbacks in the East, the Franks and their new faith could grow.
I suspect that it isn't that the Franks were that successful in projecting power as it is that the people who were successful in projecting power happened to be the Franks. Kind of like the lottery; someone will win, and the identity of the winner is more important than the specific forces that caused those numbers to bubble to the top of the pile at the exact instant of the drawing.
I'll assert without evidence that human organization tends to oligopoly - an even balance of power is unnatural, and once you cross a certain boundary the balance of forces shift in favor of gaining even more power. (difficult for a coalition of 25% power to contest with a coalition of 75% power). Someone was going to win, and it just happened to be the Franks.
Geography, population, culture, climate, all play a part, as do things that are more difficult to measure (relative strength and charisma of leaders at inflection points, etc.). It is somewhat useful to study those factors, but in no way can you develop a useful model for prediction or even for analysis. There is too much (literal) chaos to permit modelling.
I acknowledge in advance that this is a bad answer because it provides no sources and doesn't fully answer the question. I thought about it and decided that it was worth posting.
I consider it a result of what I call the "oyster" phenomenon. (Oysters produce pearls because of the irritation provided by sand.)
The Franks in France were the largest standing force in western Europe; other tribes existed, but were weaker. Because of their relative strength they became stronger and turned the tables on others, instead of crumbling under the various pressures, the strongest of which came from the Moors to the south. This strength was because they were a Germanic tribe that had merged with the Latinized Gauls, and had the combined advantages of both German "freshness" and Roman civilization. This relationship went all the way back to the 5th century, that is, about three centuries.
They were fortunate to have leaders such as Charles Martel, and his grandson, Charlemagne. The process began when the Moors invaded Spain, then France, and were defeated at Tours by Martel, who counterattacked, and drove the Moors out of France and back into Spain. Later, Charlemagne's (French) empire was the target of Saxon raids, so he retaliated by invading and occupying most of what later became "West" Germany.
Finally, French projection of power into England resulted from the raids of the Norsemen, who went to Normandy, and from there to England after intermarrying with the French.
It really is that simple. Having read the answers so far, I feel that in some ways the point is being missed. There is a fundamental human interaction that I'll paraphrase this way: if you walk into a room and act like you are in charge, you are until someone proves that you are not. I don't know if I have any Frankish ancestors, mostly my line comes from Danes, Yorkshiremen, Germans, Hungarians, Serbs, and we think a bit of Swiss. But that little point boils down to:
It seems to have worked as a philosophy for the Franks and their successors the Normans. (I mean, really? The Normans took over the Kingdom of Naples and the two Sicilies?)
I don't think it is all that complicated. Atilla the Hun, one can argue, succeeded under a very similar philosophy, and look at how well he did.
