The USA started development earlier
Generals fight the last war. In the muddy trenches of WWI, the major semi-automatic rifle designs such as the Mondragón Modelo 1908 and the FAM 1917 rifle that you mention proved to be difficult to keep clean enough to operate. Though the FAM 1918 performed well in the Rif Wars, we actually observe FAMs converted from semi-automatic to bolt-action when they were handed over to colonial troops. Given the mood around disarmament at the time, we can assume that the focus for the Great Powers was on colonial policing, rather than preparing for another total war.
As a result, France's next rifle development was also bolt-action, intended to be a cheap gun for colonial troops. The French intended to follow up with the MAS-40 semi-automatic, but the design was only completed in 1949 (at which point it did serve as the standard issue rifle for a decent length of time).
Meanwhile, the USA was working on the Garand as early as 1922.
The USA also had more time to adopt the new design
Even the simple MAS-36 had a very small production run before the war kicked off - only 250,000 were available for the Battle of France in 1940. Even if France had a design like the MAS-40 ready to go on the same day the USA began production of the Garand, it would not have been able to produce it in sufficient numbers. The UK did the same calculus, and when war was imminent it focused on ramping up the tried and tested Lee Enfield rather than try and rush a new design.
It was no cakewalk either for the USA to produce Garands - at first they were only making 10 rifles per day and the army was only fully equipped by 1941. However that was more than good enough because the USA was not at war until that point, and also did not need to replace rifles lost in the field like Britain, France, and the USSR would have.
The USSR only worked out the kinks with the SVT rifles by 1940. By the start of the war, it had not produced sufficient rifles to arm even one third of their forces with it, and many were lost in the first months of the war, requiring the Soviets to fall back to using simpler and cheaper weapons.
War showed the deficiencies of all rifles, including semi-autos
The flaw with the semi-automatic rifle became apparent as soldiers gained experience in the field: they were a weapon designed for long-range marksmanship, which was not how actual battles were fought. The heavy weight and recoil of these guns was a liability with no upside.
The capabilities of rifles such as these were rarely exploited
to their fullest, with the chaotic realities of warfare (limited visibility, targets behind concealment or cover, etc.) meaning that most engagements took place at far shorter ranges than anticipated
Nevertheless, the nations fielding these weapons already had the designs and more importantly the bullets, and they were still better than bolt-action rifles, so they kept being made.
Despite the limitations of full-power rifle cartridges, significant logistical and economic investment had been made in these calibres, and these investments, along with idealized military doctrine and the exigencies of an ongoing war, meant that innovation was met with some resistance.
The Germans identified these flaws as early as 1944, leading to the adoption of the StG 44 and a new intermediate sized cartridge. The Soviets were inspired by that design to make their own AK-47. NATO countries took somewhat longer because there was a desire to standardize around one NATO-wide cartridge and gun, and in the meantime existing designs of semi-automatic rifles continued to be produced and used in line with existing doctrine.
Naturally, intermediate cartridges are not automatically (pardon the pun) better than heavy ones. In situations where it makes sense, such as for long-distance marksmanship, semi-automatic and even bolt action rifles are still used today. But from the '50s onwards the assault rifle's trade-offs fit the needs of a typical grunt better, and before the war the bolt action rifle's trade-offs fit the industrial and technological constraints better.