Modern Spanish history is one of the most interesting topics I have found. Anyway, onto an answer:

Franco approved a law of succession in 1947, saying that Spain was kingdom and would remain a kingdom. Of course, Spain would have no king while Franco was alive as he was acting head of state. The law also said he could name his successor when he chose to.

Don Juan, the heir to the Spanish monarchy, and Franco decided in 1948 that Don Juan’s son - Juan Carlos - would return to Spain to be educated in Spanish schools and in Franco’s ideology. In essence, Franco groomed Juan Carlos to be his heir.

Juan Carlos completes this education and eventually married Sofia. And in 1969, Franco named him as his rightful successor to the dictatorship and Juan Carlos had to swear loyalty to Franco’s Movimiento Nacional. The two worked together after this, with Franco guiding Juan Carlos in his new role.

Franco dies in 1975 and Two days later, Juan Carlos becomes king of Spain. Now, Spain enters the period of the Restoration of the Monarchy. Juan Carlos started to issue reforms to the government and appointed Adolfo Suarez as president/prime minister (depends on your translation and understanding of Spanish government). Suarez would become instrumental in the transition to democracy and would become the first democratically elected prime minister of Spain’s new government.

In this time, many changes occur but one of the most interesting is el Pacto de olvido (the pact of forgetting), which was a political decision by both the left and right parties to essentially forget everything that happened during the Civil War and under Franco. This pact ensured that there would be no prosecutions for persons responsible for mass suffering. Important questions about the recent past were entirely ignored, so that Spain and its politicians could look towards the future and make the reforms needed.

In June of 1977, Spain held its first elections and in 1978, a new constitution was drafted that acknowledge Juan Carlos as king.

So, to answer your question: Franco did “bequeath” the country to Juan Carlos, but only after he had been groomed in his education and sworn allegiance to Franco and his ideologies. Juan Carlos did help ensure that Spain would become democratic but most of the “work” was completed by Suarez and other politicians of the time.

Some attribute these happenings as to why Spain has largely avoided the populist movements that we see in many countries today. Spanish people still struggle with The Pact of Forgetting and it’s implications to today, like should Franco’s remains be removed from El Valle de los Caídos (The Valley of the Fallen).

Did he really have the option to assume Franco-style dictatorial powers, or was he bending to some popular demand for change?

This is a very interesting question, and I'll try to answer to it, complementing /u/NearbyConcept answer.

Now, the short answer to both parts of the question is yes. The long answer, well, get ready because I got some long paragraphs for you detailing the social and political climate Juan Carlos found when he got in the throne in 1975.

Juan Carlos had the power granted to him as Head of State by the Organic Law of the State of 1966, one of the Fundamental Laws of the Kingdom, which worked as a de facto Constitution for the Francoist Regime. This gave him the power to appoint the Prime Minister, to appoint one third of the members of the Cortes (a pseudo-parliament which enacted the Laws), the supreme command of the military, and the soft power which went with being the King. In this regard, he had the same legal powers as Franco. Now, what he didn't have was the strong base that Franco had during his 39 years in power to continue with an authoritarian regime. Because the legs that supported Francoism (i.e. the Catholic Church, the military, the fascists and the conservatives) had all lost the strength they had during the 1940s, thanks both to social changes and the opening of the Regime during the 1960s and 1970s, which occurred to face this social changes.

In 1940-50s the economy was in shambles, and Spain was living in economic isolation from the rest of the world. In 1957 the State was on the verge of bankruptcy, so Franco removed the Fascist government in place and put in charge what is known as the "technocrats", conservative men from Opus Dei that nonetheless disliked economic autarchy and wanted to liberalise the economy. This, together with the international recognition and acceptance of the Regime, after the agreements with the Vatican and the USA in 1953, allowed Spain to be open to foreign capital, which created what is called the "economic miracle" of the 1960s. Thanks to tourism and foreign inestment, the economy boomed. This accelerated the rural exodus (in 1950s Spain for the fist time had more urban than rural population), created a baby boom (in Spain, it was during the 1960s), and reduced the mortality, which created a major social shift. More population in the cities, more young people, more industrial workers (in 1970s, they were 75% of the workforce), more educated people (in 1970, alphabetisation reached for the first time 90%), progressive liberalisation of the women, mass media, etc. all of this factors undermined the traditional support of the Francoist State. They also allowed the mass population to gain economic dignity and, through the openness with the outside world, demand the political regimes that were established in Western Europe.

It was in response to those demands that the technocrats implemented some minor political reforms. They created a Social Security in 1963, and promulgated the Law of Press of 1966, which relaxed the limitations on censorship and eliminated preventive censorship, shifting its burden from the State to the Publishers. The Law on Religious Freedom of 1967 ended the religious monopoly of the Catholic Church. They also started to allow some minor cultural expressions in minority languages, like songs and books, and extracurricular teaching of the languages, even allowing from 1964 the broadcasting of a TV show in Catalan language (in the only TV channel from the times, TVE).

This changes were not enough though, and the population started pushing for political reform. During these times grew major popular opposition to the regime. The workers movements and labour conflicts, which started in 1962 with the Miner’s strike in Asturias, pushed for the creation of illegal clandestine trade unions known as “workers commissions” to negotiate with their bosses without the intervention of the only legal union, known as the “Vertical Trade Union” (because it included both workers and company owners). These commissions would later become the trade union Comisiones Obreras (CCOO), still the largest in Spain, which was later joined by the older unions UGT, CNT and others. We shouldn't forget the growing dissent on the new neighbourhoods, created to accommodate the massive internal immigration to the industrial cities, to protest for the lack of public services in the area, sometimes even roads were missing.

There was also opposition coming from the intellectuals, specially from the Universities, now with a much bigger number of students which opposed the regime on ideological grounds (as usually intellectuals do). Another major point of opposition was the Catholic Church itself, specially from the middle and lower ranks, who felt emboldened by the liberalist reforms of the Second Vatican Council and opposed a repressive regime which went contrary to the christian values, despite its official backing of the Church. Finally, the opposition from national minorities, specially from the major industrial centres of Basque Country and Catalonia, gain a lot of support all across the class spectrum. In Catalonia, the upper and middle classes pushed for the normalisation of their culture and national symbols. In the Basque Country, this "bourgeois" opposition was joined by nationalist marxist-leninist terrorism, embodied in the organisation ETA (Basque Land and Freedom). Many other terrorist groups were created during the mid 1970s, like GRAPO, FRAP, Terra Lliure, FAG, LAR; and even some ultra-right groups, like BVE, ATE, Triple A, GAE or Guerrilleros de Cristo Rey.

To face this opposition, the technocrats wanted to increase the legitimacy of State, so they made the regime to stand on more firm legal grounds pushing for the Organic Law of the State. They also increased the repressive apparatus of the State by creating the Court of Public Order in 1963, which would be in charge of judging political crimes. The Political-Social Brigade (the secret police), the Civil Guard and the Armed Police (urban police) reaffirmed their role as executing forces of the Regime by beating demonstrators, torturing detainees and executing or imprisoning those in the opposition.

At the same time, the Francoist apparatus was divided into two main factions. On the right there were the “immobilists”, whose radical right-wing was known as the “bunker”, mainly formed by the most senior members of the National Movement (Franco’s “political party”, the only legal one). Their main figure was Admiral Luis Carrero Blanco, Franco’s right hand man and veteran of the Civil War. On the right there were the “aperturists” or “reformists”, whose main figures were Manuel Fraga Iribarne (technocrat Minister of Tourism), Torcuato Fernández Miranda (Secretary of the Movement and professor of Political Law of King Juan Carlos) and the young Adolfo Suárez (director of the public tv and radio RTVE).