Car free Sunday and Gare de Midi

Nope, not without a reason such as transporting a sick person and you have to apply for a permit if you want an exception. You do get free onward train travel with a Eurostar ticket and STIB public transport in Brussels is free that day. Taxis are exempted so if you live somewhere without public transport, you can use a taxi which can only travel at a snail's pace that day.