Firstly, tickets. As covered in this Travel.SE question, unless you have a Lille-Brussels season ticket, you need to buy your Brussels-Lille or Brussels-Calais tickets several days out, and online. (Exact slightly complicated details in this answer)
As Brussels Midi station, when checking in, there are now two checkin areas. The main (normal, long standing) one is on the ground floor, but is now for UK-bound passengers only. The special Lille checkin desk to the left has gone. Passengers for Lille and Calais need to check in at the special Schengen checkin area up on the first floor.
After checking in on the upstairs floor, you go through to a special waiting area. There is no Business Premier lounge here, and no access to the one in the main area below. (Only standard / economy tickets are sold for Brussels-France, so there aren't many people affected).
At boarding time, passengers for France are escorted onto coach 18, the one at the very back. Security guards in red shirts ensure that they don't enter any other coach, and prevent them from going past the toilets in the vestibule between coaches 17 and 18. As such, there's no access to the buffet car.
On arrival into Lille and Calais, more security staff are waiting by the exit from coach 18, with that area of the platform roped off. Passengers are required to exit at their stop, and exit through the special roped-off area back into the normal station. The train won't leave until all the French domestic customers are off coach 18.
No UK-bound passengers are permitted in coach 18, and you can't pick it as your seat, so there's no mixing of Schengen-domestic passengers for France and passport control cleared UK ones. UK-bound passengers seated in coach 17 aren't allowed (by the same red-shirted security staff) into coach 18, no matter how much quieter it might be, until after the last stop in France.
See also my answer on FlyerTalk and this FlyerTalk thread I've contributed to.