Hi
When I take cabs in London with my kids, they don't have car seats either... actually last time, they had one, but the driver could just not fix it and we lost 10 minutes one our journey to St Pancras, to take the Eurostar to Paris!
I have checked on the website of a big taxi group in Paris (taxi G7) and they say it is not a legal obligation for children to travel in a car seat in a taxi, and not an obligation for the taxi to provide one. I suppose your concern is rather about safety, but at least you will not risk a fine!
If it is just a short journey to your hotel, I would do it by cab with the child on my nap. Otherwise, it is true that the metro is really not convenient with children, buggy and luggages (you may not find anybody to open the door to pass with the buggy, there are a lot of stairs and nobody will give up space in the metro for you to put your buggy).
You can also try the buses, they're not too bad and you have space for buggies. Have a look at the ratp website to prepare your journey
http://www.ratp.fr/en/ratp/c_21879/tourists/
Enjoy your week-end!