I am assuming that English has died out and somehow our civilization has been lost as well. In other words, it's not just that we moved to some other languge and kept records of what happened in our past when we spoke English. So I'll assume that our civilization has fallen into ruins.
First, archaeologists would look at our ruined buildings and other types of infrastructure. They would see that we had huge cities and that we had an extensive infrastructure of roads, railroads, etc.
Second, they would look at whatever they could find of the contents of our houses or, perhaps, the contents of our landfills. They would use those to see what sort of material conditions we lived in--what kind of stuff we ate, what sorts of appliances and tools we had.
Between these things, they would be able to know a lot about our society.
Assuming also that future generations had the same or better technology than we have now, it's probably safe to say that American life is incredibly well documented. Emails, websites, blogs, digital photos by the billions, all of these would still exist in some retrievable format to give future generations an idea of what our society was like. There is much more evidence, that is to say, than there was of Ancient Rome or Egypt, for example, and consider how much we have discovered about them.
Add to that the masive amount of physical documents and books, records, archives, along with the architecture, buildings and evidence of our industrial society that would survive for quite some time in the future to be studied. I think future generations would have a lot of our history to study and learn from.
Powerful question. I teach my seventh graders about the concept of a Trace Fossil, a remain that shows an animal's or organism's pattern of behavior or aspect of their existence. Trace fossils are evidence of life. I use this for students to identify an object in their own life that could be a trace fossil. They write about this and link the object to their own life, their own experiences, the experiences of a culture that they define, and how other generations 300 years from now would be able to formulate understanding about themselves and the culture that the object represents. This might be how future generations could understand our own civilization if English was not an option. The objects we leave behind, what is found after we are gone, can help to tell our stories even if we, or our language, are not there to dictate it. In the end, we are what we love and this becomes powerful when this can narrate our own story to those who are unclear of who we are and in what we believe.
Knowing a language spoken by a group of people, definitely helps in understanding the finer points of culture and civilization of those people. But most of the characteristics of a civilization can be completely and correctly described by any well developed language. As a matter of fact, we can learn from books so much about all the different ancient civilizations without knowing anything about their language.
It is interesting to note that the English that people know and speak today is very different from the English spoken a thousand years back. This has not prevented us from studying and learning about the civilization of English Speaking that existed a thousand years ago. Also different language are spoken in different parts of world. But that does not prevent people of one region learning about civilizations in other parts of the world.
Another important point to note is that though English as used today may die out as a living language, just as some languages like Latin and Sanskrit have. But this does not mean that there will be no one who can understand English, making it impossible for anyone to make sense of any records in English language that will survive the language itself.
Finally, I believe as and when English dies out as a language, it will only be to make place for a better language, more suited for recording and explaining everything and anything including nature of earlier civilizations.