I believe you've already had a lot of replies in the Facebook group.

Hello, I appreciate that this information is likely too late to be useful, but just for other travelers who might be wondering about the same thing. If you're trying to avoid seat reservations, then opt for traveling solely on regional trains instead of high-speed international trains like the Thalys. Unfortunately, most trains in France do require reservations, but you could use regional InterCity and TER trains to get from Bruxelles-Midi to Paris. Also look out for regional TER trains to reach the French-Swiss border. You can read more about avoiding reservations in France over here.