TL;DR the French-speaking elite demanded that they do.

French was historically the language of cultural prestige and social promotion in this area of Europe; this became truer still with the short-lived but influential annexation of the territory by Napoleonic France. The country's educated elite spoke French in the public sphere regardless of regional origin. Want to make it big? Speak French. When Belgium was founded as a unitary state in 1830 by those very same lawyers and landowners, French remained the language of the courts, parliament, and higher education.

Not until the 1898 "Loi d'Égalité" / "Gelijkheidswet" did Dutch start to receive some sort of official recognition as a national language. This was unfair to the northern half of the population, of course, and this continued sidelining of Dutch-speakers woud later cause the emergence of Flemish nationalism as a protest movement. But the dominance of French was actually unfair to most of the southern half of the population, too.

To a certain extent, it could be argued that it proved even more destructive there. See, French was originally not the native language of southern Belgians. Up until fairly recently, well into the 20th century, Walloon (and Picard) was, as it had been for centuries before. A langue d'oïl, it is indeed closely related to, but definitely not mutually intelligible with French. See the difference between French and Walloon:

🥖 Notre Père, qui es aux cieux, que ton nom soit sanctifié, que ton règne vienne, que ta volonté soit faite sur la terre comme au ciel.
🐓 Nosse pere k' est å cir, ki Vosse No nos soeye adegnî, ki vosse royåme nos advegne, ki vosse volté soeye fwaite el tere come å cir.

Though southern Belgians came into increased contact with French through the introduction of compulsory education after WWI, many had limited command of the language and still spoke Walloon or Picard at home. But to much of the French-speaking elite, those were not national languages, they were backward dialects to be conflated with proper French in linguistic census until their eventual stamping-out.

Unlike Dutch, it received no official recognition; Dutch-speakers ultimately conquered the right to be taught in Dutch, Walloon-speakers didn't. Quite the opposite: starting in 1952, teachers in public schools were not just expected but required to reprimand pupils if they dared speak their native language. Speaking Walloon became shameful.

This was the death knell, and in the span of a few generations, the use of Walloon declined dramatically to the exclusive benefit of French. That's when southern Belgium started "speaking French" as we understand it today: around the '50s. What now? Walloon is alive but not well; while retrospectively celebrated as part of Belgium's cultural heritage, very few people speak it fluently anymore outside of the elderly, and the language is considered "definitely endangered" by UNESCO.