The expression "Roman holiday" had a much less pleasant meaning before the Audrey Hepurn film. Since ancient Romans entertainments such as gladiator contests involved a lot of blood and gore, the earlier use of "Roman Holiday" meant pleasure derived from watching barbarous acts or others' suffering. Eventually any violent public disturbance or scandal could be called a Roman holiday, even if it wasn't the kind of pre-planned thing you could buy tickets to watch.
"There were his young barbarians all at play;
There was their Dacian mother: he, their sire,
Butcher'd to make a Roman holiday!"

Lord Byron, Childe Harold's Pilgrimage, Canto iv. Stanza 141.

Merriam-Webster dates the phrase from 1886, but this may only reflect how long it took to become relatively common, since the Oxford English Dictionary says the phrase originates in the Byron poem quoted above, which was written in 1818.

There was also a British band called Roman Holiday who had some minor hits in 1983 but broke up after their second album in 1984. A different band, based in Virginia, now uses the name.