The Arabs were traders and merchants, not settler colonialists. They did not conquer the Canarians, for instance, despite the Canarians being a close "European" equivalent to Native Americans (linguistically and culturally they were relatives of the Berbers). They did not settle uninhabited islands either, for the most part, hence why Madeira, the Seychelles, and the Mascarenes were not settled by Arabs, despite their clear knowledge of them. So this begs the question as to why the Arabs would go after the far more challenging matter of settling the Americas.
But Morocco was nicely located and OTL expressed interest in acquiring colonies in the Caribbean. But a Moroccan Caribbean colony on a lesser sugar island which is protected due to an alliance with the English is a bit less than colonisation of the Amerias.
I did this once in Medieval 2 Total war. Using the Moors faction based in North Africa, I invaded the Aztec Empire with a combined army consisting of Arabs, Berbers, mercenary Turks, Sudanese Africans, as well as Tlaxcala mercenaries from the Americas.
More seriously, one might imagine that you'd get a significant Berber element to the population as Morocco is genetically mostly Berber and Arabisation did not reach current levels until fairly recently. It's possible you'd get Berber spoken in parts of the Americas as a result. It's also interesting to speculate what effect various types of preachers could have on the development of strange, heterodox versions of folk Islam across the American content/s. It's likely we'd see all sorts of mystical versions of the faith emerge and syncretic practices surviving in some regions (just as happened with Catholic Christianity in some parts of Mexico).
The Moroccans (and their offshoot Andalusians) are definitely the most likely. But there is the oddities of Berber Islam, be it the more mainstream sorts or the entirely unique varieties like Barghawatism, plus the attested effects of Berber Islam in West Africa to consider. Overall I think that with the effects of Old World disease and the scarce numbers of New World natives north of Mesoamerica, you'd be substituting Christianity with Islam for the effects on native beliefs. Unless this invasion/colonialism happens in the 13th century when the Mississippians were at their height, then the numbers of natives wouldn't collapse as hard and more syncreticism can occur. Or an outright attack on Mesoamerica.
Berber would definitely be spoken, yet would be a secondary language since they'd be encouraging Arabic to be spoken instead. You'd have a situation comparable to New Sweden and its majority Finnish population or Canada and its Canadian Gaelic speakers. The long term survival and success of Berber languages depends on linguistic policies in the colonial government and motherland, but getting some Berber-speaking areas in the New World, if not an entirely Berber-speaking country or two there, is very much possible (and even more likely than back in North Africa).
A few issues are that Morocco's population is smaller than Europe, and also the point of departure from the Arab world to the New World is much narrower. The rest of the Arab countries are further away to the east. Thus I'd imagine smaller numbers than in Europe's OTL conquest. That could mean more native assimilation and survival. Perhaps it might look a bit more like the Spanish-speaking parts of the Americas in the sense that more of the native population would survive. Although it could also be quite different, as I don't know if the Arabs would have transported so many black Africans to the New World (they may have, or they may not, I just don't know).
The Canarians will be incorporated first and foremost into the Moroccan state, before any New World expedition is launched. Madeira and the Azores will be settled as well, and Cape Verde too if they're going the southern route. The Moroccans can go north using the ocean currents and wind up in the Bahamas and East Coast of North America (and perhaps Bermuda too), or go south and wind up in West Africa and Brazil. I think the southern route is more likely, since the politics of Saharan states could make the trade routes across the desert expensive enough to go for a radical option like sailing down the coast to West Africa instead.
I think they'd be involved in something like the slave trade, since the Moroccans grew a lot of sugar and such and there's plenty of crops which will do well in the Deep South or Brazil which slave labour (which the Moroccans were already involved in) enhances. Although the Muslim beliefs regarding slavery will make things interesting in that regards. Their "easiest" settlements will probably be the Caribbean. I don't think they'll get to conquering Mesoamerica.
It would be interesting to see Moroccans in the Deep South adopt yaupon tea as a trade good. It was used as a tea substitute many times in American history (notably after the Boston Tea Party where it was a symbol of patriotism and exported as far north as New England, but most often because people in the area it grew were too poor to buy normal tea). It was also maligned as causing vomiting because indigenous people would mix it with lots of water and emetic herbs in religious ceremonies. Still, yaupon's relative yerba mate (of similar religious significance to American Indians) was important locally. The Moroccans OTL have enjoyed tea for many centuries, so I wonder if TTL they avoid the issues of the tea trade with the Orient and go for their own "local" caffeinated drink (which they'd export to the rest of the Muslim world as well as Christian Europe).
We could see people of European descent still being the majority and Berbers fleeing south to Mexico to escape persecution.
What do you mean? Displacing the Arab/Berber colonists who have been there for generations will be challenging, and the Americas are huge. If Europeans thoroughly evicted them, they could just flee across the Appalachians, and once they're in OTL Ohio/Kentucky/Tennessee, they're pretty much set. No need to go to Mexico.