Have tried again to get an ID and the closest that I can find is:

7 mm Galand Short Case / 7 mm French thick rim / SFM 10400 (30-08-1895) / SAA 1875 / XCR 07 013 CBC 010
From the MuniciĆ³n site.

The case is slightly longer than the Galand short, and shorter than the Galand Long.
However; the rim diameter, rim thickness and base diameter correspond reasonably well.