Spain wouldn't get an edge in the space race then. Now with all seriousness, I've read such scenario in a book called "Virtual History of Spain" from which the authors extracted a series of conclusions. First, on the day of his assassination Carrero Blanco was going to a meeting to discuss the so-called "Association Law" which IOTL Arias Navarro passed on January 1975. This law wasn't particulary relevant, but maybe it would get a quicker implementation. Blanco would continue to act as president of the government until Franco's death in November 1975. Blanco was more of a Francoist than Navarro, so the regime would have been harsher between 1973 and 1975 and with Blanco as an unifying force the pro-Francoist elements wouldn't decompose as hard as they did IOTL. Overall, the feeling after Franco's death would be that Blanco would be a second Franco.
However Carrero Blanco stayed as president mainly because of his affection to Franco, stating that "I can't leave this man, it would be a desertion". Blanco was on his 70's already and was pretty tired from all the work he had to do as president. After Franco's death, Juan Carlos was crowned as king. The political views of Juan Carlos and Carrero Blanco were quite opposed, with Juan Carlos wanting to restore democracy and a parliamentary system while Blanco firmly opposed any kind of democratic reform. However Juan Carlos was the commander in chief of all armed forces, and thus would be avobe Blanco both militarily and politically. Eventually Carrero Blanco would have to step back and renounce the government, no matter he opposed the king or not.