To improve their synthesis and ultimately realize the technical promise of two-dimensional covalent organic frameworks (2D COFs), it is imperative that a robust understanding of their structure be developed. However, high-resolution transmission electron microscopy (HR-TEM) imaging of such beam-sensitive materials is an outstanding characterization challenge. Here, we overcome this challenge by leveraging low electron flux imaging conditions and high-speed direct electron counting detectors to acquire high-resolution images of 2D COF films. We developed a Fourier mapping technique to rapidly extract nanoscale structural information from these TEM images. This postprocessing script analyzes the evolution of 2D Fourier transforms across a TEM image, which yields information about polycrystalline domain orientations and enables quantification of average domain sizes. Moreover, this approach provides information about several types of defects present in a film, such as overlapping grains and various types of grain boundaries. We also find that the pre-eminent origin of defects in COF-5 films, a prototypical boronate ester-linked COF, arises as a consequence of broken B-O bonds formed during polymerization. These results suggest that the nanoscale features observed are a direct consequence of chemical phenomena. Taken together, this mapping approach provides information about the fundamental microstructure and crystallographic underpinnings of 2D COF films, which will guide the development of future 2D polymerization strategies and help realize the goal of using 2D COFs in a host of thin-film device architectures.