"White Spaniards" are the guys who think the crown should go to the Bourbons down in Spain. Orleanists want the line of Louis Philippe I to take over. The White Spaniards are just delusional and there's no serious movement to bring them back to power. The Orleanists are represented most prominently by Action Francaise, a bunch of fascists who take their cue from the deranged ramblings of an antisemitic nazi collaborator and who owe their existence to the old french antisemitic leagues.