The most common French cases often have loose latch screws.
Take a toothpick or skewer and blunt the end. Then insert it into the hole as shown and break it off.
This leaves some material for the screw to hold on to.
Use a needle to poke a hole fairly deeply into the center of the toothpick.
Turn in the screw…
Done. You may want to use a little Elmers white glue to glue in the toothpick, for extra security.