Per Bloomberg TV at 6am Tuesday (22-March), Brussels airport will be closed until tomorrow (Wednesday) morning at 6am. Unfortunately, for alternatives, Eurostar has canceled all operations within Belgium today. Thalys train between Amsterdam Centraal, Brussels and Paris Nord will also not be running today. AA customers may have to rent a car and drive to Paris or Amsterdam if travel requires them to depart today.
EDIT 611am EDT - border between Belgium and France reportedly closed temporarily by Bloomberg TV.