Mayan Indians speak a form of the Mayan language. The Mayan language family has about 28 different dialects. Most Mayan Indians also speak some Spanish. A number also speak English.A large number have come to the United States as illegal immigrants. They periodically return to their homeland.he Aztecs speak Nahuatl. The Incas speak Quechua. The Mayas speak various Mayan dialects including Cholan, Quiche, Yucatec and Lacandon. Edit. Share to: Mark Swarthout. 775,875 Contributions. Contract attorney. When not working I teach karate, collect stamps, write books, and play the ukulele.