Occupying Lutèce carried multiple significances: economic, political, and strategic. To some extent, the degree of control over Lutèce would even influence the future direction of international politics.
The downfall of Charlemagne and the subsequent division and occupation were already set in stone. Whether the people of Charlemagne liked it or not, hated it or not, the outcome wouldn't change because of their feelings. Yet even so, the national pride of the Charlemagne Ethnicity hadn't fallen with the nation, and their nostalgia for the old regime would persist for a considerable time. During this period, whoever occupied Lutèce would to a significant degree be deemed "legitimate." Even if it were a Puppet government or just the occupying foreign army authorities—as long as they held the Capital, they would at the very least be seen by the public as "tyrants who seized the throne."