I don't see why the US should have shared its nuclear weapons technology with other nations. Now, British research and scientists were very valuable in the Manhattan Project, so I suppose one can argue that there was a good deal of hypocrisy in the decision to withhold information from Britain after the war (under the McMahon Act). Still, it made perfect sense for the US to do so.
Nuclear weapons were the most powerful weapons created, and until 1949, the US had a monopoly on them. Whilst Britain was a wartime ally, she was still an empire in her own right (decolonization was only just beginning), with her own foreign policy aims that were independent of those of the US (albeit aligned, for the most part). One can see that as late as 1956 with the Suez Canal Crisis. The existence of the USSR as the main international rival did not mean that it was guaranteed that the US and UK would always see eye-to-eye in global politics. That's even more true with France and the US. Sure, they were NATO members, but nations can always leave NATO (which France ended up doing), and in any case, NATO started up as a mutual defense treaty rather than the sort of highly cooperative military structure that it is today.
Of course, Britain developed their own bomb and tested it in 1952, whilst the French would do their first test in 1960.
Now, the US was certainly more than willing to station US nuclear weapons in other NATO countries throughout the Cold War (and through today). These, however, are American warheads guarded by American personnel, though in certain cases they might have been carried by non-American aircraft in the case of a nuclear war (German and Italian Panavia Tornadoes, for example, are capable of carrying US nuclear bombs).
The Atomic Energy Act of 1946 strictly controlled both atomic material and information. This meant that even Britain and Canada, who were our partner nations on the Manhattan Project, would receive no information or material with which to develop their own nuclear programs, whether they were for weapons or not.
The below quote from James Newman and Byron Miller, who helped to draft the act, seems to illustrate the rationale quite well:
The information section of the Act reveals the atavistic depths that have been stirred by the release of atomic energy. The response to this greatest of all triumphs of scientific method and creative intelligence has been in some respects closely akin to the practice of magic among the most primitive of tribes. Having in their possession a fearful image of the god of war, which makes them stronger than all their enemies, the tribe is obsessed with the fear that the image may be stolen or duplicated and their exclusive claim to the deity’s favor lost. So a temple is built, ringed about by walls, and guarded by untiring sentinels. Those whose function it is to attend the deity are carefully chosen and subjected to purification rites; they are forbidden ever to look upon the whole image or to speak of what they have seen. They are guarded with unceasing vigilance, and at the slightest sign of defection condign punishment is visited upon them.
While fear of espionage may have played some part in this decision the actual discovery that individuals were providing atomic information to the Russians did not occur until 1949. It is also difficult to separate peaceful industrial applications of the atom from destructive uses. The effective difference between a nuclear reactor and a nuclear bomb is moderation of the chain reaction and the resulting energy output.
This was amended by the 1958 US-UK Mutual Defence Agreement, at which point information and materials were shared between the US and UK.