The triumph of Franco's Nationalists in the Spanish Civil War did not abolish the monarchy. When Franco was amassing his political coalition to fight the war, he promised the Alfonsine Monarchists and Carlists (monarchist factions who differed in who was the rightful heir to the throne) that Spain's monarchy would be restored upon Nationalist triumph in the Civil War.

However, after the Spanish Civil War, Franco was hesitant to fully restore the Spanish monarchy. The abdication of the Spanish throne by King Alfonso XIII in 1931 meant that his son, Juan de Borbon, had become the heir to the throne. Franco, however, did not trust Juan, in part because Juan was known to have politically liberal sympathies. Franco was concerned that a restoration of the Alfonsine/Bourbon monarchy would put Spain on a path toward liberal democracy (a not-so-unreasonable fear). However, conservative monarchists constituted a significant faction within Franco's political coalition- their aid in his accession to power had been crucial, which effectively meant that if Franco wanted to retain his hold on political power, he was going to have to acquiesce to a full restoration of the Spanish monarchy. In 1947, a "referendum" was put before the Spanish people to turn Franco's government into a "regency", with Franco reigning as "Regent of Spain" for life. After his death, the monarchy would be fully restored and a Spanish king would succeed him as ruler of Spain.

Franco had allowed the restoration to go forward on the condition that Juan not be given the throne. Instead, a compromise was reached whereby Juan's son, Juan Carlos I, would become king instead. In order to ensure Juan Carlos's political loyalty, Franco demanded that the Royal Family keep their distance from their son throughout his upbringing- Juan Carlos was sent to military boarding school, where Franco could supervise his political education.

There isn't a clear consensus from Spanish historians on whether Franco had any foreknowledge of Juan Carlos's democratic intentions. Most histories argue that Franco probably had never suspected a thing and, if he had known of Juan Carlos's ambitions to turn Spain into a constitutional monarchy, he willfully chose to ignore it. This was because by the late 1960s, Franco had lost almost total control of his personal dictatorship- the liberalization of the Spanish economy, begun in 1953, had slowly passed political control from the old guard of conservative monarchists to a new generation of technocrats, who were able to vie for political control as Spain's economy continued to boom throughout the 1960s. By the late 1960s- early 1970s, Franco was in extremely poor health and could do little to manage the affairs of state. Therefore, Juan Carlos began making arrangements with the reformist wing of Franco's coalition, the aperturistas, to begin a transition.

However, we shouldn't look at the transition to democracy in Spain as only the work of benevolent elites. When these plans were first discussed, it was not clear how far democratization in Spain would go. The anti-Francoist movement had slowly been rebuilding since it was decimated in the Civil War and the early 1940s. From 1956 and through to the 1960s, the student and workers' movements in Spain were very active and their organizational efforts forced the state to respond to a changing Spanish society. While organizationally led by the Communist Party, the anti-Francoist movement (especially the workers' commissions) retained a diverse alliance of political dissidents- ranging from socialists, to Christian democrats, and social Catholics. These groups tended to be, on the whole, republican and desired to restore the republic of old.

With Franco's death in 1975, negotiations with the anti-Francoist movement and with republican parties returning from exile began in earnest. The political atmosphere of the time was largely one of compromise- Spaniards, perhaps exaggeratedly, were so fearful that another civil war could be sparked that they were willing to make some big compromises. The left (comprising mostly the socialist PSOE and the even the Communists), were willing to sacrifice the restoration of the republic in exchange for a speedy transition to a full democracy, which included rights for Spain's autonomous communities, long ignored in Spain's liberal past. Meanwhile, the political right demanded that there would be no judiciary trials or retaliatory measures taken against them for crimes committed during the Franco regime. This was the compromise that was reached and thus the modern Spanish state was born.

Sources:

Stanley Payne, The Franco Regime, 1936-1975

Javier Tussell, Spain: From Dictatorship to Democracy

Raymond Carr and Juan Pablo Fusi, Spain, Dictatorship to Democracy (confusing, yes but both are definitive works)

Joe Foweraker, Making Democracy in Spain: Grassroots Struggle in the South

Pamela Radcliff, Making Democratic Citizens in Spain: Civil Society and the Popular Origins of the Transition, 1960-1978

Spain Transformed: The Franco Dictatorship, 1959-1975, ed. Nigel Townson