The map attached above shows the ethnicities of North-Central Europe during the 9th century AD. As can be seen a large part of modern Germany was at that time inhabited by Slavic-speaking peoples, who were usually called Wends by their German and Danish neighbours. The area which was already at that time German-speaking is known as Old Germany (Altdeutschland).
Within Altdeutschland, there exist just two main clusters of German people. South-West Germans can easily be distinguished from North-West Germans using PCA. Interestingly, Danish populations overlap with North-West Germans.
What distinguishes Altdeutschland from the Ostdeutschland (East Germany) is that East Germans usually harbor high levels of Slavic or Baltic (in case of East Prussia) ancestry. Slavic-speaking populations living between the Elbe and the Vistula rivers, mixed with - and partially were assimilated by - German settlers during the course of the Late Medieval Ostsiedlung:
If you are interested in learning more about the Ostsiedlung, it may be a good idea to first read Helmold's "Slavic Chronicle".
For example these three chapters:
"(...) Count Adolf started building the castle of Segeberg and fortified it. Because the land was ravaged, he sent messengers to many regions, namely to Flanders, Holland, Utrecht, Westphalia and Frisia, with a message that if they needed more land they were free to come with their families, and they would be given a lot of good fertile land, full of fish and game, rich in vast pastures. He also told Holsatians and Sturmarians: 'Aren't you the ones who conquered Slavic land and obtained it through deaths of your brothers and relatives? So why should you settle as the last ones? Be first, start migrating to this desired land, settle it and benefit from its resources' (...). After that call, huge crowds of people from various nations started coming, together with their families and property, to the land of the Wagrians ruled by Adolf, who promised to give them land. Holsatians were given safe areas to the west of Segeberg, near the Trave river, including the Zuentineveld [modern Bornhöved] fields as well as everything between the river Schwale up to Agrimesov [modern Grimmeisberg] and up to Lake Plön. The region of Dargun [modern Warder and Ahrensbök/Stoob] was settled by Westphalians. The region of Utyn [Eutin] was settled by Hollanders. The region of Süsel [south-east of Eutin] was settled by Frisians. The region of Plön still remained depopulated for the time being. Regions of Starogard [Oldenburg] and Lutjenburg as well as other areas along the sea coast were left for farming to the Slavs, who now had to pay rent to Count Adolf (...)".
"At that time Slavic lands were ruled by Margrave Albrecht, also known as the Bear, who - thanks to God's grace - managed to conquer large Slavic territories. He captured entire land of Stodoranians, Brezans and many other tribes living at the Elbe and Havel rivers. And he was crushing those of them who were trying to rebel against his rule. When decimated Slavs started to slowly disappear, Albrecht sent messangers to Utrecht and to lands along the Rhine river and also to those who lived along the ocean's coast and suffered a lot from violent storms of the sea - namely Hollanders, Zealanders and Flemish people - and he brought many settlers from among them, and he settled them within Slavic towns and villages. Thanks to that colonization by foreigners, the Bishopric of Brandenburg and Havelberg increased its strength, because the number of churches and tax income increased. But also southern banks of the Elbe were at that time colonized by Dutch newcomers, they settled lands near Salzwedel and Balsemerland [around Stendal and Halberstadt], and Marscinerland [between Arneburg and Werben], with many towns and villages, extending as far as the Bohemian Forest. (...)"
"(...) Heinrich, Count of Ratzeburg in the land of Polabian Slavs, brought masses of Westphalian settlers, in order for them to settle in the land of the Slavs. And he divided the land between them. And they built churches, and they started paying taxes from their farming income for the Glory of God. And God's deed started to spread throughout the land of the Slavs under Heinrich's reign, and was completed during the reign of his son, Bernard. On the other hand, Holsatians who settled in Wagria after expulsion of local Slavs, were very zealous when it comes to building new churches, and were very hospitable, but they avoided paying taxes. (...)"
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But what about the Central German cluster? Does it even exist? It seems that the answer is no. People with recently mixed ancestry from northern, southern and eastern regions of Germany may represent such "Central Germans", but if we only include people with all ancestors from the same region - I'm pretty sure that such people will plot within one of the 3 main German clusters I identified above.
This map shows which regions are parts of which of the 3 clusters from the PCA above:
As for the Central French cluster - it does exist (see the PCA from my post about the Pyrenees).