At the beginning of the first world war they plotted all military operations using these giant pins. Later in the conflict ‘map pins’ were developed and these ‘land pins’ became obsolete. Another fascinating example of how the horrors of war pushed technology forwards in civilian applications.

Looks like piece of a wheel and an axle from a tractor or a truck or something.

Marking the exact center of France

It looks very rough, it could be an unfinished part: a fusion that hasn't received the subsequent machining.
Maybe a flywheel.

A large ship engine valve? Maybe an unfinished casting? Finished ones here

I wouldn't have known it was metal just from the picture. It looks like a stone bird bath.

What does the top look like?

It is flat (and round obviously).