The truth is yes and no.
The political parties that supported Franco were:
After the Civil War, many people that supported Franco asked him to restore the monarchy while Falangists asked to reinforce the relation with Mussolini and Hitler.
Franco took into account everybody, however, Mussolini pressured Franco not to return the power to the monarchy because that will have benefited the UK. Franco used cleverly his steps. to Gain time (whole WW2) in order to not slight Mussolini and Hitler and giving the power to the Falangists. The end of ww2 will decide which is gonna be his next step.
In 1938, Don Juan de Borbon (alfonso´s son) decided to join nationalists to fight the republicans, in spite of having support in the army, was decided to escort him to the French frontier until the civil war ended. In 40s, Don Juan de Borbon, tried to deal several times with franco without any success until 1947. Finally, in 1948, Franco accepted to deal.
Franco was a general out of politics and the chosen one as a consensus man of the nationalists, in contrast, with Hitler and Mussolini. Franco´s prestige was so high in order to be the chosen one. Mola and Sanjurjo (the only men with more prestige than him died at the early civil war).
In the period of the Second Republic:
The conservatives were the major supporters of the monarchy while Socialists and communists were republican supporters. The liberals were extremely weak and divided.
spanish election 1936: