In short, there's no difference in the meaning of royal and royale.
In English-speaking countries, "royale" is occasionally used instead
of "royal" in order to add some element of sophistication. Instead of
naming a store the "Royal Boutique," the owner might call it "Boutique
Royale."
Royale is sometimes used instead of royal where there is a prohibition
on using royal because it might imply connection with or endorsement
by royalty.
"Royal" is used to described masculine single words while "royale" is
for feminine singular words.