Not Paris, but I lived in an even larger metropolis (Beijing) for 6 years, with two young children, without a car. We took public transport and/or rode bikes most of the time, and took taxis when neither of those were possible/convenient. Even with the taxi fares it was much cheaper than owning a car.

> Another negative aspect is that cyclists do not use public transportation,

For short trips maybe, but as a cyclist myself, I'd say cyclists are among those most likely to use public transportation for any trips that are beyond their cycling radius, or where cycling isn't feasible, instead of a car.