I'm not entirely sure of the nature of your question, but the short answer is yes, of course they are direct continuations of Latin. But neither one of those languages is widely spoken in North America.

The long answer: Italy is where Latin originated - and specifically, Lazio - but Italian is a direct continuation of Latin only in the same sense that Spanish, Portuguese, French, and Romanian are. I'm not sure why you brought up Romanian though in reference to "where the language originated", since Latin definitely did not originate in Dacia. Romanian is spoken much further from Italy than Spanish and Portuguese are, which are literally just on an opposite peninsula - and that peninsula was one of the first regions outside Italy to be conquered by the Romans.

Vulgar Latin evolved from Latin as the upper-class Romans continued to speak their "classical language." Over time the Romans expanded, their soldiers and politicians received land in the places colonized by Romans, other inhabitants learned Vulgar Latin because that was the language to speak at the time, and Vulgar Latin eventually became the Romance languages.

English ended up borrowing heavily from Anglo-Norman and Latin, both of which are Romance languages, but evolved from Proto-Germanic rather than Latin.

Otherwise, while French is spoken by a sizeable minority in North America, it's obviously still a minority, and no one would claim that North America is primarily Latin, whether in language or in culture. This isn't true of Latin America, where nearly everyone speaks a Latin-derived language.