We can have Denmark-(Norway) get more involved in New World expeditions, recolonising Greenland and taking a place in the fur trade by the mid-late 16th century. That's a pretty vague setup, since this nation (we'll call it Vinland) could end chipped away by the English or others and wind up with as little as St. Pierre and Miquelon or as much as Canada and most all the US east of the Appalachians (with perhaps bits of New England, Upstate New York, etc.). Let's go for a healthy middle ground and assume that Denmark-Norway is going to be a weaker colonial power than England is, since they have more issues with their neighbours than England does. They're also weaker than France as well. I think it's reasonable to assume that England can seize the Hudson Bay trade, as well as organise New England colonies and in general colonies on the East Coast, so expansion west and southwards is difficult. The Great Lakes leads southwards via portages to the Mississippi watershed, but how much of that will fall under control of a power which will presumably center around the St. Lawrence compared to whoever gets New Orleans? Still, the Old Northwest makes a fantastic borderland between Colonial Vinland and whoever colonises New Orleans, and perhaps later a colonial/post-colonial power seeking to expand west of the Appalachians. I agree with all the historians and others who state that the Appalachians were the most formidable barrier to expansion in US history, so it's by no means likely any East Coast power will be a threat.
So let's just go with a modest estimate of Upper Canada + Lower Canada (borders are all watershed borders anyway), the Maritimes, Newfoundland and Labrador, most of Maine (Kennebec or Penobscot Rivers make the best partition I think), and bits of Vermont around Lake Champlain and Upstate New York around the northern Adirondacks. Assuming development, immigration, etc. which is similar to Canada, or maybe even better, this place could have 20-25 million people. This is about as much as all North Germanic languages combined, and far more than any individual Norse language. I don't know what their language would sound like, but probably more Danish than anything.
And let's spruce this up as well with a Louisiana which is actually more extensively colonised, and let's go with France doing the job as they failed to in OTL. They can strongarm everything west of the Appalachians up until they meet Spanish borders. But looking at Spanish Texas and how empty it was, the fact we have Louisiana is getting more extensive settlement, and the evolving Spanish-French relationships, it's pretty likely border re-adjustments will occur. The Rio Grande border as is now is taking quite a bit of land. If these events coincide with the Pueblo Revolt, or maybe later during the worst of the Indian raids on New Mexico, Spain might as well just thrust their Indian problem onto France. In the event they don't cede land that far west (could be as far as the continental divide even), maybe something like the early Mexican western borders. You could end up with Alta California being the only Spanish province north of OTL's Mexican borders. Getting access to the Pacific is hard, but I think it's reasonable to assume there would be a huge push to work something out regarding Columbia and come up with the good ol' 49th parallel north as the border between French and English colonies.
It goes without saying that this nation, assuming it remains one state, it would be the most populous French-speaking nation in the world (at least until the population explosion in Africa, but it isn't like we have to have a scramble for Africa, and even so, most of those Africans aren't native French speakers anyway). Other possibilities aside from this (probably not at once) would be maybe a successful France-Antartique which keeps the Portuguese bottled up in the Brazilian Northeast while taking most all of Brazil's Southeast and South regions.
For the Dutch, it would be interesting if we could have those regions become Dutch ("Hollande-Antartique") or somehow have a more successful Dutch Brazil to have a major Dutch-speaking state. Maybe that's possible in this same timeline as well?
An interesting factor might be minority languages like OTL's Canadian Gaelic. Maybe we can assume in this United States/British North America, a large population of Irish speakers (few hundred thousand maybe) is able to hold onto their language, moreso than in Ireland proper, which would make the majority of native Irish speakers be in the New World. Maybe also even with Breton and Louisiana, though you didn't list Breton. It probably would be mainly elderly people by the modern age, though. I suppose Scottish Gaelic and maybe even Welsh (doubtful) also have a chance as well in that manner. Maybe something like "Scottish Patagonia" (in the manner of Welsh Patagonia), but more successful, maybe in the Mexican West, maybe in Rupert's Land/(British) Columbia (lot of Scottish furtraders OTL,). In any case, it relies on the mother nations adopting a harsher stance on minority languages than OTL.
And let's assume there's independence movements, etc. as well, since we've been assuming similar trends and all. So in the final analysis, we have the following languages which meet your challenge, plus a few others:
*North Germanic languages (Vinland)
*English (United States)
*French (Louisiana)
*Spanish (Mexico)
*Portuguese (Brazil)
*Dutch ("Holland-Antartique", which won't ever be called that)
*Irish (United States)
*Breton (Louisiana)
*Scottish Gaelic (Rupert's Land/Columbia)
Of the two you named, I don't have Italian and German. I don't think those could exist in the TL above. Best case for German would be Henry the Lion's Saxony remaining undivided and from there a North-focused Germany which could have some New World colonisation, but that's before your POD. Italian I honestly have no clue, considering how shitty the 16th century was for Italy.