This is already happening today in California, a couple gigawatts of batteries are charged during the day and released in the evening to offset peak demand.
This seems high(?): for comparison, average power of French solar panels is 1.6GW (and a bit more for wind power).
The population of California is ~ half that of France, and presumably California sells power to neighbouring states too, so it doesn't seem that out of whack.
Insolation is higher in California, with the same solar panel surface you can probably get double the energy over a year, compared to France.