Mas-44
Suggested BR and place:
BR4 - semi-auto rifle, Allied tech tree Tier IV.
The Mas-44 is a gas-operated French semi-automatic rifle firing 7.5x54mm rounds and is fed by a 10 round detachable magazine. The Mas-44 is based on the Mas-40, a rifle that had been in development since 1931 and was planned to become France’s standard issue rifle starting in 1940 this however was prevented by the outbreak of the war.
In 1944 the liberation of the Mas armoury opened the possibility of mass producing semi-automatic rifles, the Mas-40 design was revised into the Mas-44 with the experience gained during the war and the fixed 5 round magazine was replaced with a detachable 10 round magazine.
In very early 1945 the Mas-44 went into mass-production with a total of ~7000 rifles made before production had ended a few months after the war had ended.
Although the rifle had many advantages over the M1 garand such as higher reliability, very easy maintenance and a detachable magazine preventing garand thumbs, the Mas-44 had only seen a limited deployment with the French navy and French commandos due to logistical and heavily political reasons.
Even though there was major shortage of M1 Garand and M1 carbine rifles in the Free French army, therefore creating a high demand for a semi-automatic rifle capable of replacing the Garand.
Further possibilities
Premium Mas-40
French partisans/guerrillas armed with Mas-40
In 1944 when the French resistance “liberated” the factory, the thugs ransacked everything from material to the rifles, they did more damage over a few hours than German occupation over 4 years.
Most of the rifles ended up on the black market and France was pressured by the Allies not to buy them back.
Because of the unfortunate turn of events, regular army units surely didn’t use these weapons, however the French resistance did use them, this is why I believe that the Mas-40 should be equipped on a guerilla squad. (ideally a female partisan squad for a little diversity)
BattlePass Mas-40
The standard Mas-40 came with an internal 5 round magazine which was reloaded via stripper clips, however some Mas-40s have been converted to accept 25-round box magazine from Chatellerault M1924/29
Furthermore the Mas-40 could accept scopes.

A 25 round magazine fed semi-automatic sniper rifle would be truly unique.
alternatives to the Mas-44
Hallé rifle
A pre-ww1 British prototype gun with detachable magazine.
Howell automatic rifle
WW1 SMLE conversion, saw limited use in WW2 with British home guard.
T3E2 Trials .276-Caliber Garand
Edit: some details were corrected by SzepWaxweiler, thank you!
While there are alternative options, none of these rifles fit the time line.
The Mas-44 is a WW2 made in thousands, not some weird prototype with less than 50 made of them so in my opinion the best candidate for BR4 rifle is the Mas-44.