According to this page, Russian and French sockets/plugs are the same "shape", but in France we use 230 Volts while the Russians use 220 Volts. Will a laptop charger and other electronics work with Russian sockets?
Yes, it should work.
Electricity supplies with nominal voltages of 220, 230 or 240 volts are in practice the same. There are tolerances of about ±10 % in the voltage (to account for the voltage drop in transmission lines which depends on the load), so devices labeled with either of these voltages will actually be designed to function on anywhere between 200 and 260 volts, give or take.
Yes, the socket delivers different voltage but electric appliances will support a range of voltages, and plug types C, E, F are compatible with the sockets.
As I'm posting this from a French laptop plugged into a wall in a Moscow apartment, I can confirm that everything works perfectly without any need for adaptors.