The core Frankish lands were always in the north of Gaul, and the major royal centres stretched from Paris and Orléans, through Reims and Metz, to Cologne: these were not exactly capitals in an administrative sense, but they were places where kings could frequently be found, and around which they moved their courts and administrators, from palace to palace, along the Oise valley near Paris or the Moselle near Metz
This excerpt from Inheritance of Rome by C. Wickham tells us that (some of?) the Merovingian kings moved around a few cities in northern Gaul (Between what was to be Neustria and Austrasia I think). How exactly (or as much as we can understand) did this work?
This is right and not only for Merovingian Kings but for pretty much any King/emperor of the HRE (the late east francia) up to the Habsburgs (1273). I know merovingians were in the early Middle Ages and France instead of Germany but I am mostly going to talk about the situations in high and late Middle Ages HRE because that’s how long this custom of a moving King has been carried on and where I know my stuff.
The reason was because the lands were large and split into roughly 300 independent domains who only had to report to the electors and the king/ emperor this was initially a Franconian custom that was adopted after the karolingians lost East Francia to the Ludolfingers (saxons) while other Kingdoms were either small enough to manage from a Centre (Petty kingdoms of England, Burgundy) or had enough infrastructure (Lombardia/Francia).
Also the western kingdoms were further developed on a cultural level. The eastern duchies were still quarreling in their old tribal manner and were under constant threat from the northern and further eastern kingdoms of Poland, Denmark, Sweden and Hungary.
The King had to travel a lot to make sure everyone knows he’s still around and alive and in a seat of power. Rumors of the king being dead when he wasn’t could happen and would have had bad consequences.
This was practicable by three means.
The king in the HRE was different from the French or English king. In most European kingdoms and Duchies the feudal oath would be between vassal and king, be it a baron, a count, earl or duke. In the HRE a Baron (ritter) would swear an oath to a count or earl (graf) and that one would swear an oath on a Duke (herzog) or Someone with an equal rank (Markgraf, Landgraf, Erzbischof) and finally only a duke or equal can swear the oath to the king himself. That means a Duke in the HRE is a lot more powerful and has little reason to be afraid of the king. The only exception being the fourth elector, the king of Bohemia, who would only swear an oath on the emperor and for a while even was the emperor.
The king would shortly after his election and the securing of all the oaths, move to Rome to be crowned emperor of Rome. The title of emperor was uninheritable and could only be given by the pope himself. Therefore he was now no longer only king of gods grace but also holy Roman emperor appointed by god himself. So he was now even above the highest clerical lords, who were Prince electors and arch bishops of Cologne, Trier and Mainz which they didn’t like at all.
Those two conditions make him essentially be the Boss of a bunch of people who don’t really want him, so he must show up to remind them who’s the boss. And when he did he would get the best room, food for him and his (usually large) posse and leave when his business was finished be it a Noble or a cleric or even a Mayor of a Free City of the Reich. It had a stabilizing effect that was absolutely necessary for the survival of the realm.
Then he had his own Castles all around the western country (Worms, Aachen etc.) the so called Palatinates (Pfalzen), there even is a special Earl (pfalzgraf) who is equal to a Duke whose job it is to keep the Palatinate when the king isn’t there (that was a lot of time). This dude was so important that he eventually got the electorate too, like the Markgrafen of Brandenburg and Meissen whose job it was to keep the borders safe.