Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
You may as well ask, "What's up with all the epigraphs?" One explanation out there is that Cooper uses Shakespeare and Byron and other passages from the works of old dead white guys as a means of legitimizing his novel as a "high" art form. We guess that's reasonable: it wasn't super-cool at this time of writing to set novels in the wilderness of the "New" World.
A more lit-nerdy, interesting explanation is that the epigraphs serve as chapter titles. Chapter Seventeen, for instance, is when the brutal massacre at Fort William Henry occurs. The epigraph is two lines from a Thomas Gray poem entitled "The Bard": Weave we the woof. The thread is spun./ The web is wove. The work is done.
These lines refer to the weaving of the strands of Fate, indicating that events were already set in motion for the massacre to occur. This echoes Montcalm's thoughts later in the chapter:
As he mused he became keenly sensible of the deep responsibility they assume who disregard the means to attain the end, and of all the danger of setting in motion an engine which it exceeds human power to control. (17.35)
Each of the other epigraphs functions in a similar way: as a lead-in to the events of the chapter. Cooper wasn't big on the whole "spoiler alert" philosophy of writing fiction: he wanted the readers to enter into each chapter with a foreshadowed sense of what was going to happen.