See here: https://en.m.wikipedia.org/wiki/Curtis_LeMay
> Towards this aim, LeMay delivered the first SAC Emergency War Plan in March 1949 which called for dropping 133 atomic bombs on 70 cities in the USSR within 30 days. [...] Air power strategists called this type of pre-emptive strike "killing a nation". However, the Harmon committee released their unanimous report two months later stating such an attack would not end a war with the Soviets and their industry would quickly recover. This committee had been specifically created by the Joint Chiefs of Staff to study the effects of a massive nuclear strike against the Soviet Union. Nevertheless, within weeks, an ad hoc Joint Chiefs committee recommended tripling America's nuclear arsenal, and Chief of Staff Vandenberg called for enough bombs to attack 220 targets, up from the previous 70.
Note that March 1949 was 5 months before the USSR's first atomic bomb test.
It's not a leap to suggest that if the USSR didn't obtain nuclear weapons in 1949, the US would have shown much less restraint than they did. And "restraint" is already not the first word that comes to mind to describe American foreign policy in the 20th century. (As for France and the UK, I don't think the US president would have worried about the UK nuking Washington in retaliation for a pre-emptive nuclear strike on the USSR).
Why? I guess the Vietnamese communists would have surrendered to the US and the country would have lived under its influence instead of the Soviets', and that's assuming Ho Chi Min would have received enough support in the first place. There's no reason to assume the US would have nuked at someone's whim.
BTW, the French and the Brits also have their nuclear arsenal. There would not have been a "monopoly".