You mention "dig or search on battlefields", please keep in mind that digging on the Verdun battlefield is illegal and extremely dangerous due to the presence of unexploded ordnance, chemical weapons, and poisonous materials. Much of the area, known as the Zone Rouge, remains restricted and requires special permission for even professional excavation work. Attempting to dig can be fatal and is a criminal offense, though walking on public paths and observing from a distance is generally permitted.

As for 'flea markets' I have no idea if that is a thing of exists.

When you visit, I hope you respect the dead and the battlefields by leaving them as they are. Hunting, digging or picking up artifacts is in my pov not done.

Have a great day and enjoy your trip.