I have personally tried walking off randomly in Paris. I didn't use any map or GPS or even my direction sense. I just kept walking randomly and I realized it is very difficult to get lost in a city like Paris even if you wanted to. You pick any direction and walk for about 15- 20 minutes and you would definitely find at least a sign post pointing in the direction of a nearest metro station, and once you are in a metro, you are in the grid, you are not lost anymore! And of course, in a city like Paris there are always people around irrespective of the time of the day to ask for directions.