At the time that the Normans took control of Sicily, there wasn't really a 'Sicilian' vernacular language. Arabic was perhaps the most spoken language on the island, and there was also a substantial Greek populace - hangovers from previous occupation of Sicily by the Arabic states of North Africa and by the Byzantine Empire, respectively. Jeremy Johns also contends that there may have been a small Norse-speaking community at some point during the Norman period, though he doesn't venture any theories as to whether it arose before or after the Normans arrived (I'd tend to think that if there were Norse-speakers there, they probably arrived after the Norman regime was established, due to the origins of the Siculo-Normans in the relatively Norse-flavoured Contentin peninsula in Normandy).

The interesting thing about the Norman occupation, linguistically, is it's likely that many of them spoke vernacular Arabic, at least by the time we get to the first generation of Normans actually born in Sicily (which was when Norman rule was established in earnest). We see that certainly by the time of Roger II (the first Norman king of Sicily), the royal diplomata (official documents) were issued variously in Latin, Greek and Arabic - probably as a concession to the strong continuing presence of those communities.

It's one of the hallmarks of Roger II that he tried to be inclusive when he was creating his kingdom. Whether this was a philosophical preference or simple pragmatism (overcoming multiple established communities with a numerically inferior Norman force and no official reinforcements coming from back home would have been a tall order) is unclear but, whatever the motive, Roger II's kingdom of Sicily strove, with some degree of success, to be a fusion of all its components. Roger himself is shown wearing Byzantine (Greek) imperial robes in some contemporary depictions, but is also reported to have worn traditional Islamic garb at official royal appearances.

My point here is that Sicily under Norman rule was very much a stew of the various component cultures, and the same seems to have been true of the languages. Palermo, the capital city, was one of the primary concentrations of Arabic community on the island, so frequent and fluent use of the Arabic language would be both diplomatic and practical.

There's a lot more to be said about the patchwork nature of Sicily's composition during this period - I could get into discussion on Caid Peter, George of Antioch and the diwan al-tahqiq, plus there's a good article about currency which I can't bring to mind right now - but as a brief overview hopefully this sheds a bit of light. Far from imposing Normanness on Sicily, the occupiers actually adopted many features of the communities over which they came to rule, and this includes language.

Sources:

Johns, Arabic Administration in Norman Sicily: The Royal Diwan

Enzensberger (ed.), Guillelmi I Regis Diplomata

Matthew, The Norman Kingdom of Sicily

Houben, Roger II: A Ruler Between East and West

Breese, 'The Persistence of Scandinavian Connections in Normandy in the Tenth and Early Eleventh Centuries', Viator 8

Johns, 'The Language of Islamic Art', Oxford Today (don't have vol./issue/date handy)