With no PoDs prior to the death of Charlemagne, how can his empire still be around a century later? What are the latest PoDs we'd need for (1) West and East Francia to be united around this time (circa 913), and (2) are still ruled by a Carolingian? Bonus points if the growth in learning, the economy, and social infrastructure seen in the Carolingian (and OTL Ottonian) Renaissance(s) are wanked as well. And once we have a scenario -- how is history changed as a result?
then if we face a scenario in which the Carolingian empire does not collapse in itself, but even "prosper", we must necessarily focus on the last decades of Charlemagne's reign, from the death of his brother Carloman and his conquest of the Lombard kingdom, we see in Frankia an ever-constant growth of the economy, population and knowledge ( in part obviously due to the end of the continuous plague epidemics that hit Europe since 540, the other cause is naturally the formation of a more or less centralized state for the era and the region involved, which favors the rebirth of trade and the uniformity of knowledge ( both for the training of new bureaucratic personnel i.e. the clergy ( 1 ) but also to unite the various populations, all different from each other ), all also favored by the cessation of conflicts in the heart of the kingdom, after the conquest of Lombardy, a concept well before 800 AD was established in the Carolingian court itself, that is, that of Charles as a revived Constantine, also favored by his conquests and triumphs in the name of Christianity ( in practice the presumed break with the past due to his coronation in Rome had already been present for at least 20 years before ( 2 ) if the Empire were to survive longer it is very likely that a concept of Frankish ethnicity as the single glue of the empire would take hold more than in Otl, especially if we consider that the Ottonians, although of Saxon lineage, were very active in bringing out their policies as directly continuous with the Carolingian ones ( particularly in the Rhine regions and in Italy, as well as in the numerous interventions in West Frankia or Lotharingia ), naturally a more cohesive state that is not torn apart by internal strife can easily oppose the Magyar and Viking incursions ( if we consider that Otl France when it had a strong enough ruler was able to stop the raids on the coast immediately, I don't see why a stronger state couldn't do equally ) this is also the indirect result of increasing the Romance-speaking population of the empire as a whole ( which in the long run can become another important glue for its unity ) once again the weakness of the Carolingian emperors seriously begins to appear from peace of Verdun from 843 onwards, and then increased dramatically in the following decades ( with rare exceptions ) this could also partly favor the papacy, which would avoid one of its worst historical periods ( pornocracy, which really began with the collapse of central power in peninsula since the death of Louis II the Younger in 875 and the establishment of competing local dynasties ) this will also massively influence the development of Umayyad Iberia and Catalonia ( which under Louis the Pious was firmly under Frankish control, also because it was the place where his father had sent him to train ) and the eastward push of the peoples Germans ( until 900 the Bavarians were pushing into the Pannonian plain before being violently stopped by the Magyars ( 3 ) I also consider possible a previous expansion into the Slavic regions beyond the Elbe ( Otl Charles deported some of the last rebellious Saxons there in 804, furthermore in the last years of his reign he had engaged the armies of the empire in campaigns against the Danes / first Vikings ) therefore military actions on that front are quite likely, without forgetting the passive influence that the Franks exerted across the Channel ( 4 ) which was quite discreet lastly, a long-lasting existence of a fairly cohesive state to the east of Byzantium can provide a greater incentive for the latter to collaborate with it (it had already been done at a basic OTL level against the Bulgarians and Avars ) and ultimately propose a matrimonial alliance ( 5 ) between the two heirs of Rome ( although it may create discussions, I consider the Frankish empire a very just heir of Rome, since it brings together the Roman-derived traditions developed in the late Western empire with a political project, all carried out between the Roman church / papacy and the Germanic people most romanized ever ( and has survived the challenge of time, managing to effectively unite the new ( the Frankish rulers and their traditions ) with the old ( the Gallo-Latin population, the surviving Roman laws and administration, the clergy and the remaining Roman nobility etc )
P.s
Furthermore, I believe that not giving birth to Charles the Bald could at least partially mitigate the power struggles between Louis' eldest sons, given that it was his insistence on including him in the division of the empire that caused years of intense civil conflict because at least before then the other brothers had agreed to recognize Lothair as their supreme lord ( and the territories assigned to him were originally larger, see in particular the imperial division of 817 )
1 ) an example of this are the councils that Charlemagne called in 799 in Aachen and in Tours in 813 to standardize the beliefs and education of the ecclesiastics ( who also functioned as important bureaucrats in the empire, as they could read / write and count quite well ) see also the foundation of the Schola palatina in 780
2 ) indeed according to some historians, this idea was much older, given that Pepin and his sons were appointed by the pontiff as Roman patricians ( i.e. protectors of Rome ) in 751, which was then further sealed in 757 ( Pepin's last expedition to Italy against the Lombards )
furthermore, according to recent studies, Eginard's work was in fact written between 814 and 830, considerably late compared to the contested methods of the coronation, since the other contemporary chronicles agreed on the fact that Charles was anything but surprised and against at the ceremony. Both the "Annales regni Francorum" and the "Liber Pontificalis" report the ceremony, speaking openly of celebration, maximum popular consensus and evident cordiality between Charles and Leo III, with rich gifts brought by the Frankish sovereign to the Roman Church, it was, only later, around 811, in an attempt to attenuate the Byzantine irritation for the imperial title ( which Constantinople judged to be an unacceptable usurpation ), precisely in the " Annales Maximiani " was the element of revisiting the past concerning " the surprise and irritation " of the sovereign
3 ) I also consider the future development of the proto-Romantic languages in the Balkans interesting, since Otl, many of them were formed or disappeared in this period, see for example the Pannonian language which disappeared soon ( in the tenth century it remained only around Lake Balaton, in present-day Hungary ), while the Romanian language established itself in the Carpathian area, which gradually differentiated itself from the Italian group of the Adriatic, while in the 11th century the Aromanian group originated in the southern Balkans ( with the existence of a predominantly Romance-speaking empire in the West, how will these languages be influenced, could we perhaps see the court of Aachen try to attract these populations ? )
4 ) this soft power was very strong in Kent and Mercia ( although the relationship between Charles and Offa was at times stormy )
5 ) something already previously sought by Irene ( first for her son Constantine VI then for herself ), with the failed engagement between Louis II and one of Theodora's daughters, the widow of Emperor Theophilus in 843 and then the more successful attempts of the Ottonians Otl
