Do ancient people communicate in classical Chinese in their daily life?

No, ancient people used the social spoken language at that time to communicate in their daily lives.

According to the purpose, "language" can be divided into two categories: daily communication language and written language.

The language of daily communication is called "spoken language". With the influence of social and economic development, economic and trade exchanges, population mobility and migration, ethnic integration and many other factors, spoken English changes almost all the time. This change is slow and gradual. If we intercept it according to the times, we can find its obvious differences. For example, the so-called "ancients" in the question covers the predecessors in history. They live in different historical periods and use different spoken languages.

Written language, called "written language", is specially used for writing articles, that is to say, the existence form of written language is not "words" but "texts". Such as classical Chinese, vernacular Chinese and so on. It exists in articles and works in classical Chinese and vernacular Chinese. Written language comes from spoken language, but it is relatively independent of spoken language and has its own development law. Its changes are often rapid. For example, the written language-classical Chinese, which originated in the pre-Qin period, once formed, remained almost unchanged except for some new substantive words. Because classical Chinese is gradually divorced from spoken language, this will inevitably lead to "change" from the Tang Dynasty, when some people tried to write articles in spoken language. In the Song and Yuan Dynasties, storytelling flourished. In order to make people at the bottom of society understand it, the written language of vernacular came into being. The four classic novels in history are the representative works of this written language. Because this kind of vernacular Chinese is based on the spoken language in Song and Yuan Dynasties, it is more and more different from the later spoken language, and the vernacular Chinese has changed again in the last twenty years or so. People call the vernacular Chinese in Song and Yuan Dynasties "ancient vernacular Chinese" and the newly reformed vernacular Chinese "modern vernacular Chinese". After the founding of New China, the pace of language reform has been accelerated, and now the written language is different from the modern vernacular. People call today's written articles "modern".

The fundamental difference between spoken and written language lies in different forms of use and different purposes. People use spoken language in daily communication and written language in articles. Although written language comes from spoken language and constantly adapts to the changes of spoken language, there are always differences between them. For example, the written language "Modern Language", which is closest to modern spoken language, is not an oral communication language. For example, public figures can use written language when they "speak" on specific occasions, but what they usually say is still spoken. For another example, the classical Chinese in the pre-Qin period was close to the spoken Chinese at that time, but the "ancients" at that time did not say "classical Chinese".

In a word, classical Chinese, vernacular Chinese and modern Chinese are all "words", which belong to written language, not communication language in daily life. The dialogues of characters in costume movies and TV plays that people see are all "literary". In fact, it is the atmosphere carefully created by the creator, and no one really understands the dialogue between the characters. Even the ancient "quotations" recorded in ancient books have been modified by the author of the book. For example, Zhu Yuanzhang's words recorded in Ming history are not true.