Why didn't they just subsidize bike and bike lock purchases for individuals?
What is great with this program is that you take the bike only when you need it. You don't have to carry it with you all the time. You can combine subway, bus and bike. There are a lot of stations around Paris. You can use the bike one way only if it is raining for example, and use the bus/subway to go back.
You can do the same thing (though not quite as convenient) with a folding bike.
They could put a plan in place to offer incentives for people to buy some standard folding bicycle. Folders are expensive because there aren't too many produced and because they need to be fairly light, however, mass-produced they shouldn't be too expensive.