The "magical" event that happened mid/late 1950's was that autarchy was still not working and the other main faction of the government (called technocrats, mainly the Opus Dei) said "the national catholicism is cool and all, but we need to get profits and this autarchy shit isn't working". So the autarchy ended to the Falange dismay, and the country slowly opened economically and started catching up with Europe.
Sadly Falange is on the rise again (falangist Buxadé from Vox cleaned the party from capitalists in the last couple of years), and you can hear young people calling for closing and going "Spain first" again.
>Shortly before the end of World War II and the later beginning of the Marshall Plan, President Roosevelt ordered the American ambassador in Madrid to inform Franco that any "political or economic aid" from the United States would be "impossible" as long as the dictator remained in power.
>The decision was ratified in August 1945 by a joint declaration of Stalin, Truman and Attlee. In February of the following year, France closed its border with Spain, leaving the country completely isolated. The UN asked all its members in December 1946 to retire their ambassadors from Spanish territory, and did not revoke its condemnatory declaration until 1950. Spain joined the UN in 1955
[...]
>The government protested against the isolation, stating that Spain had "the right to buy on international markets", and criticized the international community for sabotaging the country's "right to live according to its spiritual values"
>The Spanish international reputation would begin to improve gradually in the late 1940s and early 1950s, after the consolidation of the Cold War, due to the explicit interest of the United States in promoting anti-communist governments in Western Europe. The diplomatic displays of approval by the American government helped to strengthen the regime and stabilize its economy, which would eventually lead to the liberalization policies that marked the 1960s
Which is exactly what I said in my previous reply. Isolation FORCED by the international community (Franco fought against the USSR and Cold War wasn't established yet), they embraced it sure because they had no other choice. They could trade with Argentina (Franco-Peron protocol, signed in 1946)