Weapon cover/bag

Hi all..
Picked up these two Gun bag/action covers.. any ideas what they were designed to fit!!!???????

Made of heavy duty canvas with leather reinforcement, closure is by post and eyelet with a Leather "lace" that passes all the way through.... the central panel can be left open leaving just the front and rear sections fastened, this is why I thought perhaps action cover????
Thery seem to be possibly early (natural leather) and late types (green leather) or merely manufacturers differences?? The natural leather one, has Part?? Numbers..54.070.672 500 and a possible maker and date HBC 61' it also has a name "GILL" in marker....
 
The other example has no markings...



look forward to your comments and ideas....many thanks

Paul

They are certainly French, but I am not sure which rifle fits.

Thanks Andrew!!! That narrows the search down a bit!!!!
Cheers

Hello

It is used with the french FM 24/29 cal. 7,5mm
the model with natural leather parts is the older one , "61" is the manufacture year

Salutations

Many thanks...but... i still don't understand why it has the leather reinforcement and protrusion at the rear... a couple of inches from the butt end!!??
The AA 52??(never seen one before!!)also known as "la nana"!!!!!????..... looks like an airborne version MG 42!!!(trigger group looks identical!!) with extending buttstock!!