Emelie's sniper rifle is a Mosin-Nagant M91/30 PU. This is a Soviet weapon which would have been found on the Eastern Front and highly unlikely to show up in Southern France (or anywhere in France for that matter). Even the ability for her to get ammunition (during the war) would have been near impossible.
In the shot of the C-47s (Dakotas) flying to deliver the 517th, the plane in the foreground is numbered "62" - the plane to the rear right (obviously a CGI) is also numbered "62". The 3rd plane in the shot (also CGI) is so blurry as to not be able to identify the nose. In actuality, all such planes would have had different numbers.
The film takes place during World War II, which ended in Europe on May 8, 1945. The "Airborne Creed" was created in 1946, when the first dedicated airborne training facility was built by the U.S. Army.
The first paratrooper seen landing fires back to the pursuing Germans with a naked bore weapon,presumably a M1A1 carbine,yet in the prior and following scenes he is carrying only an M1 Garand rifle. A better look at this scene shows that the character Rossi returned fire with a carbine, the character Curtis had the M1 Grand and landed just after Rossi. The camera jumps back and forth between them creating this confusion. They each retain and use their respective rifles throughout the film.
The telephone shown on the German officer's desk is an American-made North Electric telephone. This is evident in close-up, when the American-style dial is clearly shown.