I have had an interest in the Berthier, since my teen years, when a friend inherited a three-shot Ste. Etienne made carbine.
We never got to fire it because the ammo was a collector's item. But, the petite carbine was a cool piece of machining and fun to handle!

I never fired an arm, chambered for the 8X50R cartridge, until the Prvi Partisan factory ammo came onto the U.S. market.
The Prvi (Full Metal Jacket) factory rounds, I have measured, appear to have a .327" projectile.

In the last 12 years, I have owned and fired a couple of nice Berthier carbines, which I 'flipped' for a good profit.

I briefly had a 'cut-down' (Remington made) Berthier rifle that was too altered for 'reasonable' restoration. I sold it, for what I paid.

My project Berthier rifle was built at Chatellerault, in 1917. Although the rifle received the (post WW-1) "N" chamber alteration, it has proved to be the most accurate Berthier, I have fired.

The Prvi 198 grain soft-nosed projectiles, I purchased, are measuring a maximum diameter of .325". It remains to be seen, how they perform. This is my first experience reloading this cartridge.

Although a .325" diameter bullet appears to be undersized for French rifle bores, on the "Gunboards Forum", knowledgeable participants have reported good success and accuracy with .323" diameter bullets of U.S. manufacture.