you are wastly overestimating how much money could be saved in this manner - The primary reason I expect the changeover to electric to follow very hot on the heels of the first reasonable electric car to hit the market is that electricity is much, much cheaper than gas.

Math: Let us assume that you are a foster parent in France, take care of nine kids, and thus you drive a monster of a people mover with a onehundred kwh battery, and you go through one charge per week. Top it off to full each night during generic offpeak hours, and you are out 8.75 euros /week. Most of which is, in fact, taxes. Which you cannot avoid by messing about trying to time the electricity market. So, at most, if you watch the weather reports like a hawk, and plan your driving very carefully around them, you save.. 2 euros per week. 104 euros per year. And this assumes that you are driving the electric equivalent of a SUV. For a smaller car, it is going to be half that.
Nobody is going to actually do this - it is far too much work for far too little return - Certainly it will not be common enough to affect overall demand at all. The day/night demandshifting works because it is automated and transparent to the consumer - Plug in at night, charged by dawn.