But what if Louis the Child had been a strong, competent monarch? How would a longer Carolingian dynasty have affected East Francia and Europe?
The problem was less having a competent monarch, than the general political and social crisis of Carolingia. Late Carolingian kings of WFrancia were generally competent enough to at least stand their ground for a while against northern French nobility, especially Robertians that already took once the throne at this point, and still went down.
Basically, the rise of Carolingian potentes and the threat they were for the effective maintain of the Carolingian dynasty was already well in progress and would make a surviving Louis of Germany as under pressure than Charles of Western Francia. Survival of the Carolingian dynasty in Eastern Francia isn't impossible, of course, but it would be messy and possibly quite divisive within Germany and Lotharingia for a while.
It could arguably be the reciepe for having a more divided, politically-wise, Germany at the exemple of what existed in Northern France (limited exemple, of course, would it be only for demographical and density differences). You'd argue that Ottonian (or Arnulfian, for that matter) exemple points that it was expectable for Germany to take back the imperium, and with good reasons (namely that Italy was in a poor political state, and Western Francia less and less able to intervene at the south of its own kingdom, while Carolingians generally found a loyalist base in Aquitaine). But how Ottonians "cleaned their orbit" IOTL might not be that reachable for EFrankish Carolingians, if it happens roughly like in WFrancia.
As for the consequences in Europe, I doubt Charles would focus less on Lotharingia : his elections IOTL was a "divine surprise" due to the end of Carolingian line, but he depended too much on it to abandon it (altough, depending on the situation, you might end with yet another glorified treve), which could arguably make Charles III reign not that affirmed, but less unstable (while bickering about Lotharingia isn't really going to stop).
