First of all, welcome to Flyertalk!
If you're just hitting Vienna and Paris, I would strongly suggest
not taking a car seat since it will mostly just sit in your hotel room. It will be of no use at all on trains and subways since there's no where to attach it.
Taxis are another matter. Many people in big cities simply skip the car seat in a taxi. Look
here or
here (or do a search of the forum) for more opinion and options. The consensus seems to be that, if there's no where a taxi goes that a bus or the subway doesn't, you're better off with public transportation. In Paris and the close suburbs, this is the case as it is with most of the standard tourist attractions in the Paris region. I assume it's true of Vienna as well but will let someone with firsthand knowledge weigh in.
Have a great trip.
Michael
p.s. if you do end up renting a car, many of the rental places will throw in a cheap car seat for a couple of euro a day. I wouldn't rely on it if I were planning to rent, but if you do it on a lark, you'll at least have the option.