I have to ask... what is so important about Brussels and Brabant that the French were willing to literally commit voter fraud to control it? It's not at any strategic location for defense like Nice and Savoy, nor is it a very rich port city (again, like Nice), and doesn't have any natural resources I'm aware of. France only control Brussels once, during the Revolutionary and Napoleonic period. So what is it about that damned city that makes it so valuable compared to, say, Namur (capital of Wallonia), especially when it's on the periphery of French interests?
IMO France would want Brussel for many reasons
First, it was the former capital of the Belgium Kingdom and control it mean more prestige, they took a former capital of kingdom and it also symbolic by being the capital of the kingdom by saying it and take it it would mean that the kingdom joined the country and that Flemish made secessions and not the opposite.
Secondly, Brussel is a strategic place because all the former infrastructure in the kingdom was built with the perspective of Brussels as capital by controlling it you have access to a lot of infrastructure for a next war
Thirdly Bruxelles was saved by the French at least in their propaganda, so it would be logical that they kept the city in term of militarist point of view, they control it by retroceding this to the Dutch it would imply a failure in terms of diplomacy a submission.
Fourthly, Brussel controlled by the enemies would mean a huge city heavily fortified that would make a conquest in the Netherland more difficult in terms of war or here it would be the opposite it would make a aggression of the Dutch more difficult.
Fifthly, more territories are always welcome, and Bruxelles was always an important city the Princely Capital of the prosperous Burgundian Netherlands, by controlling it you avoid that this symbol falls in the Netherlands hands. Brussel was also taken by France but ceded to Austria in a treaty of peace so you could find a way to retake lost land (especially with the theory of Natural border Bruxelles should be French (French culture (at least in the upper class) according to many French nationalists)
Sixthly It was also a work of local elite so maybe french followed the movement or genuinely believed that Bruxelles wanted to be french, and that they need to rigged the elections in the neighbour territories to avoid an exclave that would impact negatively the city.
You could find a lot of reasons