No, they most definitely don´t! America, my friend, is a continent. Time for your free geographical lesson. You have North America, and South America. In North America you will also have Canada. They mostly speak French and Canadian English. After that, you have South America, with a wide variety of languages. So, FYI, there is no language with the name American.
What they speak as a general language in USA, is US English or American English. Something that creates the fact, that you speak UK English or British English. End of lesson. No need to say thank you! 🙂