Hi Stew, as Corrina posted there is an automated bike rental system in place in Paris. It is called Velib.You must have a micro chipped CC to use, which as a Canadian you can obtain if you go to your bank(Canada is switching to chipped cards but some cards/banks are doing it very slowly, so just ask)
I would also say try a FT bike tour, the night one is especially fun. You do not spend alot of time waiting for anyone as part of the trip to riding a bike in heavy traffic is that the group must stay together "like a bus, or like the Tour de France", as guides explain it safer to travel looking like a big unit... its actually an ongoing joke, "hey, stay with the bus, they won't run their car through a whole group of us" mentaility.
You do not book ahead or anything, just show up,, really .
Anyways, renting a bike from Velib looks fun too, but the traffic during day does look a bit daunting,, but hey, millions of French people ride bikes can't see why you couldn't. Have fun.