The French were actually first. MAS made a semi-auto rifle of gas impingement design in 1940 and there was some limited production as the Mle 40 before the German invasion. The Mle 40 used a fixed box magazine like the Mle 36 and was loaded with a stripper clip. In late 1944, after the Germans were driven out, MAS revised the design to use a detachable magazine, and it was adopted as the Mle 44, but only some 6200 were produced. After a few more revisions, the rifle was adopted and widely issued in 1949, becoming the more familiar Mle 49, of which 20,600 were produced.
The rifle was again revised in 1956 and the Mle 49-56 adopted. It is that rifle that made up the bulk of imports into the U.S.
See
http://www.carbinesforcollectors.com...iflepage1.html for more info on French rifles of the cartridge era.
The Swedish AG-42b (the Ljungmann*) was early also; I don't know if Ljungmann was inspired by the MAS or worked out the idea independently, but the design is quite similar to the French. I don't recall any FN impingement design; theirs all were short/intermediate stroke piston systems.
Stoner came along later, but where the earlier impingement designs opened at the top to vent exhausted gas into the open air, the Stoner designs channel it through the bolt carrier and out the ejection port. The design has been subject to considerable criticism, but certainly appears to work well enough.
*The Hakim is a licensed copy of the Ljungmann, made in Egypt in 8mm Mauser caliber; the Rasheed is a carbine, in 7.62x39, which uses the Ljungmann gas system but has features of the SKS.
Jim