You have to remove them by hand or hoe/rototill the crops and use mulch to keep them from coming back.
if that doesn't work, you plow them under and replant.
we grow organic rice here in the Philippines... you know all those wet rice paddies? It was for weed control.
an organic farmer should already know,
1. you keep weeds cut below 6 inches height for fire prevention and to eliminate pollen spread, and
2. you get rid of weeds by spraying them with vinegar when the ambient temp outside is between 70-90degrees, and
3. to prevent anything at all growing for a year or two on fallow fields, you add salt to the vinegar
organic farming doesn’t mean you get to pollute your neighbor’s fields with weed pollen and seeds