Unknown WW1 Overseas, Campaign Hat?

[Obal7]

I need some help to identify this suspected WW1 Overseas, Campaign hat. I recently got this from a US WW1 soldier along with a grouping of WW1 medals and such. I'm still trying to research this soldier but preliminarily it seems that he may have been with an artillery or ordinance unit with the 32nd Infantry Division. Along with the typical US medals and ribbons, he seems to have been awarded a few French medals. Along with this, was a very good conditioned Trench periscope.

The Campaign hat is a bluish grey type of cloth, no tags or markings except the dark blue/black added piping around the edges. Also a brass type "pin holder" for some unknown badge , rank, unit?
This does not look like the typical Campaign/Overseas hat that A US Doughboy would wear?
Any help would be greatly appreciated. If I find out anymore info, I will let you know.

[bigmacglenn]

WWI French Garrison Cap...
cheers, Glenn

[Obal7]

Thanks Glenn!! I kind of figured that it wasn't US... Like US Piping, in your opinion, do you think the black/dark blue piping mean anything..a unit, branch?

[reneblacky]

The US type is based on the French design!

[Obal7]

Thanks for the info..Do you know , what pin/emblem, possibly could have been on the hat?