One more thing to consider. Typically, cars in Europe do not have the anchor system found in the US cars that make it easy to get the car seat in and out. Also, their seat belts do not automatically lock in. So you have to bring the little peice that takes up the slack in the seat belt. Otherwise your car seat would be useless.
We brought a car seat for the taxi rides in London and Edinbourgh. Taxi drivers were very patient while we installed the seat. It was not so much a pain as we used the taxis only to get from/to the hotels from/to the airports/train stations. We used public transportation otherwise.
Not sure if that is possible in Paris and Brussels.