You throw it out of your window onto the street, where it is collected by men and brought to waste mounts outside the city gates. There also was a sewage system which led to the river Seine, the same river from which people got their drinkwater by the way. Either way, it was a mess. People did realise that waste, and mostly human waste led to disease, although they thought it had to do with smell. So in the 12th century, there were initiatives to pave the streets and to try to dispose of waste in sewer systems. Animals weren't allowed to roam free anymore, but had to be held in place and that also relieved some of the mess.

Source: Garbage in the Cities. Refuse Reform and the Environment by Martin V. Melosi. (2004).