Expanded from an earlier answer of mine

The immediate stance of the Allied powers towards Spain at the end of the Second World War was diplomatic isolation and pressure for internal regime change. The origin of this strategy evolved out of two interrelated factors: Spain's diplomacy in the last two years of the war, and the geopolitics of the nascent Cold War.

Franco's attitude towards the war was complex and evolved over time. He initially saw the Molotov-Ribbentrop Pact as a betrayal of the ideological new order and an alliance with the enemy, communism. The Fall of France modified his view somewhat as it presented Spain an opportunity to expand at the expense of defeated France and a weakened Britain. Hitler though was relatively inflexible to Franco's demands for belligerency and Spain took on the stance of a friendly neutral. Spanish neutrality actually benefited German interests as it was a supplier of raw materials, especially the crucial industrial element tungsten, and Spain's friendly government aided the German war effort in the Atlantic and the Abwehr's espionage rings. The Allies looked askance at Spain's friendly stance to the Third Reich and developed two tools which to pressure Spain to return to actual neutrality. Firstly, there was the hard pressure of economic blockade and threats of further sanctions against the weakened economy. Secondly, the Allied intelligence networks fostered contacts amongst Spanish elites, especially within the army to push Spanish towards a pro-Allied stance. The Allies maintained a fine balancing act between these two stratagems; they did not want to push Spain into a situation in which Germany would invade, which would divert military forces of the Western Allies to defend its new-found ally. Franco reluctantly began to see the writing on the wall and withdrew the Blue Division from the Eastern Front in 1943 and announced a shift from nonbelligerency to neutrality in October of that year. Yet, Franco only really began to cut Spain's ties with Germany in a concrete fashion around D-Day. Although Spain almost declared war on Japan in 1945 over its treatment of Spanish nationals in the Philippines and even offered to allow Spanish volunteers to fight Japan, Franco's inconsistent stance towards Germany had turned Spain a pariah state by the time of the Potsdam Conference.

Spain posed a quandary for the diplomats at Potsdam and each pursued their own agenda with regards to Spain. The Western Allies had little stomach for a military intervention in Spain, which they perceived as militarily weak, but with geographic advantages that would make a resistance long and protracted. Spain also had given no real pretext for invasion beyond its ideological sympathies for fascism. Here is where the covert attempts to win Spanish elites entered into high diplomacy and geostrategy. The British desired a relatively stable and friendly Spain that would act as guarantor of Gibraltar and thus provide one less headache for the ultimately futile effort to reestablish a strong British empire in the Mediterranean. This meant maintaining a cold reserve towards Franco and the Falangists, but strengthening ties with conservative monarchists which would hopefully lead to a monarchic revolution and depose Franco. The American position was similar to Britain, but more preoccupied with a communist resurgence in Spain that might result from too of a precipitous fall of Franco.The British Ambassador in Washington summed up the State Department's attitude in a May 1945 report:

that whilst in full agreement with our policy in principle, State Department feel in practice, if we are too stiff with Franco we may give undue encouragement to Communist elements. In the present mood of Moscow they might well turn out to be as inimical to our long term interests as the Falange itself. Mr Armour [the new US ambassador in Madrid] apparently has an instruction to hasten the demise of the regime. The State Department are now thinking of telling him to ease any pressure he may have been exerting and, while doing nothing to encourage Franco to believe that anything less than drastic reforms are necessary if his Government is to gain the confidence of the democratic world, at least to desist for the time being from giving active encouragement to the opposition elements.

For the Americans, a stable Spain to prevent communism meant at least in the short-term a guarded acceptance of Franco and his diplomatic isolation to nudge him towards reforms.

The Soviets perceived the Western Allies' reluctance to deal with Franco directly and decided to capitalize it. Molotov's brief on Spain at Potsdam stressed that the current Spanish government was an artificial imposition upon the Spanish people by the fascist powers. Although his brief did not call for a direct invasion of Spain, it called for the United Nations "to break off all relations with the Government of Franco; 2. To render support to the democratic forces in Spain and to enable the Spanish people to establish such a regime as will respond to their will." This was a more radical stance than the Western Allies, but it also served as a justification for the creation of the satellite states in Eastern Europe. The Soviet's public diplomacy stressed that the Red Army acted as a liberator of artificial regimes propped up by fascism such as Bulgaria, Romania, and Hungary and the new communist-led regimes were the true manifestations of the people's will that fascism had dampened. A harsher stance against Spain would be a legitimation of the Soviet's actions within Eastern Europe. The Allies' rejection of the harsher tone also became a victory for Soviet diplomacy in that it opened the Western Allies up to charges of hypocrisy when they critiqued the lack of freedom in Eastern Europe by their toleration of an actual fascist government in their backyard. The Western Allies recognized this and sought to soften the Potsdam's declaration on Spain and not give the Soviets an issue. The resulting declaration was somewhat mild:

The three Governments, so far as they are concerned, will support applications for membership [of the United Nations] from those States which have remained neutral during the war and which fulfill the qualifications set out above. The three Governments feel bound however to make it clear that they for their part would not favour any application for membership put forward by the present Spanish Government, which, having been founded with the support of the Axis Powers, does not, in view of its origins, its nature, its record and its close association with the aggressor States, possess the qualifications necessary to justify such membership.

The lack of severity of the Potsdam Declaration was greeted with some relief in Spanish elite quarters. Martin Artajo, Franco's current foreign minister briefed Franco by saying Potsdam was " less strong than we expected in Spain and less radical than it was expected outside." Although the Western Allies' diplomacy gave Franco a cold shoulder up to the 1950s, this benign attitude gave Franco time to recast his wartime actions as less fascist and more anticommunist. Called the chaqueteo (turning the cloak), Franco's narrative was that he was a fervent conservative anticommunist that used both Hitler and Mussolini to defeat the Soviet efforts to suborn the Spanish state. Franco then had the last laugh by refusing to enter the war when Hitler really needed him, but Spain had to remain neutral because of the threat of German occupation. The chaqueteo had already found an admirer in the US wartime ambassador to Spain, Carlton J. H. Hayes This self-serving narrative meshed well with the anticommunism of the US State Department of the Eisenhower administration and Franco lost his pariah status in the West. A 1953 subcommittee report of a tour of European defenses from the House Armed Services Committee outlined the degree to which Spanish actions had transitioned since May 1945. While acknowledging some of the problematic Civil War and wartime activities of Franco, the report concluded that the communist context mitigated these actions. Franco's fight against communism made him an ideal partner for the Cold War, especially since

No amount of disguise can overshadow the fact that Spain did defeat communism. Spain preserved her integrity and she snatched away from the vultures of the Kremlin, their camp followers and dupes, one of the great strategic prizes in the world. Her reward was to be isolated for many years and frowned upon by the Western World. No wonder Spain was slow in coming to agreement. At last, sober thinking and considered judgement have swept away the fog in our international relations; and we have placed friend and foe in their proper positions. The past ought to be interred in the limbo of things better forgotten, while we devote ourselves to the future in which we all must live. The strategic potential of Spain is one of the great contributions to our global deployment needs. She has a population which is hospitable as a matter of conviction to the idea of participating in a common defense against atheistic communism.

Other elements in the American body politic likewise framed Franco in a noble light. In a 1951 book on US-Spanish relations, Hayes portrayed Franco as one who successfully prognosticated Soviet expansionism, which he asserts in 1951 is "a far more dangerous threat to our security and way of life than Germany ever was," but that short-sighted isolationist policies led to Franco having to rely upon the only partners he could find, which happened to be Italy and Germany.