If the size of ones European population decided who dominated the New World, the three big languages of the Americas would be French, German and Italian. The truth is that Denmark could have sent as many settlers to America as England and later UK, in fact around half as many Danes migrated to Netherlands as English people to the USA. Of course Denmark would be unlikely to do so, I think that if Denmark ended up controlling any prime real estate (for settlement) like the St. Lawrence River, Danish settlement pattern would look pretty similar to the French one, except it would simply continue with a few thousand settlers every decade. I also find that Denmark would have adopted something similar to the French Canadian seigneurial system, but Danes would be far more willing to live under such a system, as Denmark functioned in similar manner and farmhand often migrated to from the islands to empty tenant farms in Jutland (as Jutland tended to see greater losses in Danish wars). So if Danish landlord paid the trip and accepted the rights Danish tenant farmers had, plenty of Danish farmhands would travel to Danish America to become tenant farmers.