From what I understand, Franco made it one of his cornerstone policies to aggressively implement Catholicism in Spain, at the expense of other faiths it secularism. However, he was also a dictator who killed and oppressed people, something which I think you'd have a hard time finding support for in the modern Vatican.
So these things considered, how did the Vatican view Franco and his actions? Did they denounce him on the basis of human rights abuses? Or did they overlook this because he was promoting Catholicism?
So, this is an incomplete answer, since it's really only dealing with the early period of Franco's rule, but Eamon Duffy has this to say about the Church and the Spanish Civil War.
From 1931, the new Republican regime in Spain was increasingly hostile to the Church. With the outbreak of the Spanish Civil War in 1936 hostility turned to active persecution, and refugees flooded into Rome with accounts of Communist atrocities, the massacres of priests and seminarians (7,000 murdered within months), the rape of nuns. The Nationalist opposition, by contrast, though also guilty of atrocity, and not originally noted for their piety, increasingly saw the Church as integral to their vision of Spain. They received the endorsement of all but one of the Spanish bishops in a joint pastoral in 1937, and despite General Franco's murderous acts of repression, the papacy backed him.
There was no disguising, then, Pius XI's softness towards the right. An authoritarian himself, he saw no particular evil in strong leadership, and he valued Fascism's emphasis on the family and social discipline. When Italy invaded Abyssinia in 1935 the pope did not condemn, and delieverd speeches couched in such bewildering and lofty generalities that it was impossible to say what he thought -- it seems likely they were written by Cardinal Pacelli.
I will say that Duffy is a bit harder on Pius XI than I've seen elsewhere. After all, the Vatican was surrounded by a fascist regime and there was a general threat to Catholics in Europe. This is often given as the reason for the (rightfully condemned) Concordat with Hitler.
It's also worth noting (as Duffy does before this quote) that Pius XI was absolutely terrified of Communism. Having been in Poland as the Papal Nuncio in 1920 before he became Pope, he witnessed the Polish-Bolshevik War and came to see Communism as the greatest existential threat to Europe and, especially, the Church.
The Catholic Church fully supported and backed the military uprising of 1936 against the Spanish Second Republic. The church's support of the Franco regime remained unwavering well into his regime. In 1953, the Franco regime signed a concordat with the Vatican that recognized the legitimacy of Franco's dictatorship in Spain. The concordat gave the regime direct control over the appointment of bishops, a power Franco knew was necessary if he hoped to maintain a conservative church in Spain. In exchange for this power, the regime performed a myriad of economic and political favors for the church in Spain. The Concordat assured the church had almost total control of media and social life, rights of censorship, extensive land holdings, full control of the education system, and more.
However, this full support of the regime began to falter in the 1960s under Vatican II. As the church began reforming itself internally, a new generation of liberal priests entered the seminary in Spain that became active in the anti-Francoist underground. Many of them espoused a variety of political views, ranging from Christian democracy, to social Catholicism, to Christian socialism. The Spanish Church, which had once held to a strict traditionalist catholic view of a hierarchical caste society, now pushed a new social gospel that emphasized the empowerment of workers and relief for Spain's poor.
The dissident church was also fairly active in the Basque Country, where the Catholic Church had long connections with Basque nationalism even before the 1960s. Both the Basque Country and Catalonia had a number of anti-Francoist parishes in the 40s and 50s who aided in organizing strikes and preserving linguistic heritage. But it wasn't until the 1960s that you saw a major shift in the Church's policy towards the regime.