Personnally I ride a motorcycle; it was stolen last year and so I used bikes for about a month. Here are my observations, that I think are difficult to fix with money alone:
- pedaling makes you hot and sweaty; you arrive at the office being a mess
- when it rains you get super wet, much more than on a motorbike, because you have less protection and you don't carry special rain trousers with you at all times (whereas they're permanently stored on my motorbike)
- also, when it rains, if you cover yourself up to avoid the rain, you get even hotter and sweatier
- Paris isn't flat! (contrary to Amsterdam...) and some hills are very steep
- some distances are irrealistic for bikes: I have two clients who are 15km apart and (to me) 15km on a bike is a fairly long ride
All in all it seems bikes are mostly for tourists (who don't have to show up in an office at the end of their ride), during the summer (well, the part of the summer when it's not too hot) and for relatively short distances.
But in the absence of bikes, tourists don't take a car, they mostly use public transports (or maybe an occasional cab), so I very much doubt more bikes mean less car traffic.
There is another program in Paris that seems much more promising: Autolib, cheap electric cars that you can rent for a very short amout of time. Doubling that with electric scooters would be really great, IMHO.