In this work, a new framework of lensless Fourier transform multiplexed digital holography (LFTMDH) is proposed, leveraging the double field of view (FoV) in a single-shot recording. The proof-of-concept system with double FoV is realized by adopting a spatially multiplexing technique by inserting a cube beam splitter in the object path. The cube beam splitter divides the object beam into two FoVs with different object information. By carefully aligning and optimizing the orientation of the cube beam splitter, these two FoVs along with a spherical reference beam (generated at the object plane) are allowed to interfere with the active region of an image sensor, resulting in a multiplexed Fourier digital hologram. The object information (amplitude and phase) is obtained by applying a single Fourier transform to the recorded digital hologram, making the technique faster with the added benefit of double FoV, compared to its counterparts. The feasibility and advantages of the proposed system are demonstrated through experimental validation and comparative analysis with the existing system. The results indicate that the proposed system not only achieves double FoV imaging in a single-shot recording but also maintains spatial resolution in the reconstructed images. Its applications span various fields, such as biological microscopy, nondestructive testing, and optical metrology, where wider FoV is crucial.